摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. TRANSACTIONS OF T H E F A R A D A Y SOCIETY Founded in 1903 to promote the study of Sciences lying between Chemistry, Physics and Biology V O L 6 0 , 1 9 6 4 PAGES 1-1184 THE FARADAY SOCIETY Agents for the Society's Publications o The Aberdeen University Press Ltd. Farmers Hall, Aberdeen Scotland0 The Faraday Society and Contributors, 1964 PRINTED IN ClREAT BRITAIN AT THE-pRESs ABERDEEN

ISSN:0014-7672    

DOI:10.1039/TF96460FP001

出版商:RSC    

年代:1964

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. TRANSACTIONS OF THE FARADAY SOCIETY Founded in 1903 to promote the study of Sciences lying between Chemistry, Physics and Biology VOL. 6 0 , 1 9 6 4 PAGES 1185 -2308 THE FARADAY SOCJETY Agents for the Society’s Publications: The Aberdeen University Press Ltd. Farmers Hall, Aberdeen sco tland@ The Faraday Society and Contributors, 1964 PRINTED W GREAT BRITAIN AT TH3 VNIVERsrn’ PRESS ABERDKEN

ISSN:0014-7672    

DOI:10.1039/TF96460FP003

出版商:RSC    

年代:1964

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Factors Affecting Torsional Barriers in Benzaldehyde Derivatives BY H. G. SILVER AND J. L. WOOD Chemistry Dept., Imperial College of Science and Technology, London, S.W.7 Received 9th July, 1963 The far infra-red spectra of benzaldehyde, 0-, m- and p-tolualdehyde, and 0-, m- and p-chloro- benzaldehyde have been recorded from 55 to 400 crn-1. Torsional barriers are obtained from the vibrational assignment. Changes in the torsional barrier follow the inductive effect of substituents in the ring. The torsional vibration will absorb strongly in the infra-red when the torsional axis unites a light group having a large off-axis dipole moment with a heavy " anchor " group.The phenyl group is particularly suitable as the anchor group as it intro- duces no group frequencies below 4OOcm-1, but nevertheless has a large moment about the torsional axis. The choice of -CHO for the light group provides a large off-axis dipole moment, without adding the complication of hydrogen bonding, as would be so with, e.g., -OH. For these reasons, benzaldehyde was chosen. It was expected, and found, to have a single, strong, readily identifiable torsional frequency. The choice of phenyl for the anchor group also allows one to determine the effect on the barrier of substituents in the ring. Each substituent group introduces two low frequency bending modes per heavy atom. The methyl and chloro groups were chosen to keep the number of heavy atoms to a minimum (one).These substituents are also unlikely to introduce hydrogen bonding complications. The inductive effects of the methyl and chloro groups are in opposite directions, while the xnesomeric effects are in the same direction, and it is therefore possible to estimate the influence of these effects on the torsional barrier. EXPERIMENTAL Benzaldehyde, m- and p-tolualdehyde, 0-, m- and p-chlorobenzaldehyde were obtained from Messrs. Hopkin and Williams. All refractive indices were within O~OOO1 of the re- ported values ; boiling points were respectively, 181 (179.5), 198-9 (199), 202-4 (204), 208-12 (208), 213-14 (213), 42-5 (479, (melting point), the reported values are given in brackets. 0-Tolualdehyde was prepared from 0-tolunitrile by the method of Brown et d.,1 purified by recrystallization of the semicarbazone to constant m.p.= 212 and regenerated by dis- tilling from aqueous phthalic anhydride ; ng o-tolualdehyde, 1,5485. All the far infra-red spectra were obtained with a vacuum grating spectrometer built jointly by the authors and Mr. P. Taimsalu. p-Chlorobenzaldehyde was examined as a solution in nujol; all other compounds were examined as the pure liquids. Samples were always enclosed in poly- thene bags, and a comparison made between thin and thick samples to eliminate interference effects. RESULTS AND DISCUSSION The infra-red spectra are presented in table 1, together with Raman data.2 56 TORSIONAL BARRIERS I N BENZALDEHYDE DERIVATIVES TABLE 1 .-LOW-FREQUENCY SPECTRA OF BENZALDEHYDE AND SOME DERIVATIVES BENZALDEHYDE i.r.R. 127 m 126(3sb) 140 w 140(3sb) 224 s 225(2b) 240 s 237(2b) 0-CHLOROBENZALDEHYDE 1.-r. R 123 vs 160( ?) w 155(4b) 204 m 198(1) 247 vs 242(+) 292 s 290(2) 335 w 0-TOLUALDEHYI)E i.-r. R. 130 m l a ( ? ) w 173(0) 216 m 255 s 253(2) 329( ?) w 358(?) w 372(0) ~-CHLOROBENZALDEHyDE i.-r. R. 185 s 183(2b) 239 vs 238(0) 304 s 298(4) 329 s 2w1) m-TOLUALDEHYDE i.-r. R. :::} 127(3) 191 vs 196(2) 220(2) 251 vs 244(9 309(+) 344 m 341(1) 358 m P-CHLOROBENZALDEHYDB 1.-r. R. 104 vs 180 vs 180(1) 193 ms 247 w 243(0) 311 vs 304(2) 357 vs 350(1) p-TOLUALDEHYDE i.-r. R. 121 s 191 s- 188t2) 21W2) 244 w 315 s 352 s 347(3) ASSIGNMENT OF THE LOW FREQUENCY MODES The purpose of the assignment of the lower frequencies is to identify the torsion.Comparison with monosubstituted benzene derivatives,3 particu€arly chloro- benzene4 and toluene,s which are uncomplicated by the presence of a torsional frequency, permits a confident assignment of the three benzaldehyde bands lying below 400 cm-1. The assignment agrees with that recently given by Green.6 Although no Raman polarizability data are available, it is still possible to make a consistent assignment of the lower frequency fundamentals of the tolualdehydes and chlorobenzaldehydes. In particular, the torsion frequencies can be identified with considerable confidence. The assignment is shown in table 2, together with that for the parent compounds, used as the basis of comparison. In all cases the planar configurations were assumed to be the most stable, and the reduced moment r1, for the torsion of the -CHO group was calculated for these forms by the method of Pitzer.7 The values are shown in table 3.* The barrier parameter V2 also given in this table is obtained from the torsion frequency v by 4nzv2c2 = 2V2frIa.Vz is then a torsional force constant, equivalent to a cosine potential of period IT and curvature (d2YldQ = n12 equal to the Hooke’s law force constant corres- ponding with v. In all the present cases, the two lowest Mathieu oscillator energy levels differ very little from the harmonic oscillator ones. As the difference is much * The structural parameters assumed for this calculation are shown in the appendix.H. G. SILVER AND J . L. WOOD 7 smaller than the uncertainty in the position of the band origin, there was no worth- while advantage in using the Mathieu levels.The probable error in V2 arising from experimental uncertainties, is estimated as & 0.2 kcallmole. TORSIONAL ISOMERS The planar forms of 0- and m-benzaldehyde deriv- atives could exist as oxygen-cis-X (0-cis) or 0-trans torsional isomers. These isomers have different reduced moments of the CHO group, and consequently the assignment to the torsional isomer is necessary in deter- mining the barrier. If the stronger torsional band of m-MeB at 128 cm-1 is due to the 0-cis form, the barrier is little different from that in benzaldehyde. As little change is found in the barrier in p-MeB, where no question of torsional isomerism arises, a large change in the m-Me, as would be implied by assigning 128 cm-1 to the 0-trans form, is not to be expected.Further, if the introduction of an 0-cis Me group has Little effect on V2, the intro- duction of an 0-trans Me group will also be unlikely to produce a marked change. The shoulder of the torsional band at 121 cm-1 is thus considered to arise from the trans form. This assignment is indicated by the unbracketed figures in table 3. The intensities do not, of course, necessitate that the proportion of 0-cis form is greater than that of 0-trans, and the equality of the barrier parameters suggests the proportions are equal. The assignment of the m-C1 benzaldehydes follows by the same arguments. In 0-Cl benzaldehyde polarity and the van der Waals repulsive radii both favour the 0-trans form, to which the 123 cm-1 fre- quency is assigned. Hydrogen bonding does not appear to be important, but if present would also favour this form.There is no indication of a torsional band from the second isomer. In o-tolualdehyde the 0-cis form is favoured by polarity, and by any hydrogen bonding that may be present, but not by van der Waals' re- pulsions. There is no evidence of a second torsional band, and the assignment must be left open. FACTORS INFLUENCING THE TORSIONAL BARRIERS The barrier of 6.37 kcal/mole in benzaldehyde is in marked contrast to the triple cosine barrier of 1.15 kcal/mole in acetaldehyde 8 and suggests that the high barrier is due to the overlap of the 7r orbitals of the ring with those of the carbonyl group. The introduction of a methyl group in the ring will tend to release electrons into the ring by both the induc- tive ( I ) and mesomeric ( M ) mechanisms,9 the increased C a .- .- 9 d d 0 .r( v) Y ?5 s N8 TORSIONAL BARRIERS I N BENZALDEHYDE DERIVATIVES electron density resulting in greater overlap and a higher barrier. As the sum of the + I and + M effects of the methyl group is small (cf. the dipole moment of toluene), relatively small changes in the barrier are expected. No change is ob- served in p-Me, and small increases in m-Me and in o-Me if the latter has the trans form.Direct o-Me interaction which could stabilize the cis-0 form would also give rise to a higher barrier. Thus with either assignment the 0-result shows no inconsistency, but is indecisive, and the m- and p-results are consistent with the small influence of the Me group.compound B = benzaldehyde B 0-C1-B m-Cl-B P-Cl-B o-Me-B m-Me-B p-Me-B vtorsion ( a - 1 ) 127 123 129 (120) 104 130 128 (121) 121 TABLE 3 torsional form - 0-cis C1 0-trans C1 0 4 s C1 { 0-trans C1 0 4 s c1 0-trans C1 0-cis Me 0-trans Me 0-cis Me { 0-trans Me 0-trans Me { { { - - rlbc a.m.u. A2 9.30 11.83 9-35 9-44 10.96 9.44 10.96 10.62 11-10 9-44 9.45 10.52 9-45 10.52 10.22 V2 double mine potential parameter harmonic oscillator approx. kcal/mole 6-37 (7.65) 6-00 6.67 (7.71) 6-67 4.87 7.96 6-77 6-57 (7.32) 6.57 6-39 (5.76) (5.90) The introduction of a chlorine atom leads to strong extraction of electrons from the ring by the - 1 effect, and a smaller electron release by the + M effect, the dipole moment indicating that in the net effect, the - I predominates.It has been sug- gested that both the I and M effects influence positions in the order p>o%m.9 If so, there would be a large decrease in the barrier in p-C1 benzaldehyde, a smaller decrease in 0-C1 benzaldehyde, and little change in m-C1. The observations bear out these predictions except that m-C1 benzaldehyde shows a small, unexplained increase in V2. In general, then, the influence of the substituents on the barrier follows the ex- pectation from their established inductive and mesomeric effects. However, in the present cases the I effect is larger than the M effect, and the changes in the barrier could have resulted from the operation of the I effect alone. p-Chlorobenzaldehyde, which shows the most pronounced change in the torsional barrier, is the only compound which was examined in solution. Although Miller 10 found no change in the acetaldehyde torsional frequency on change of phase from gas to liquid, other low frequency fundamentals show great sensitivity to the environment. 11 It is a pleasure to thank the D.S.I.R. for a grant for the construction of the spectrometer, and for supporting one of us (H. G. S.).H. G. SILVER AND J . L. WOOD 9 APPENDIX The structural parameters assumed for benzaldehyde are shown in the figure. The values are composed from those of related compounds, pa.rticularly benzoic acid. Chlorobenzaldehydes : parameters as for benzaldehyde, and C-C1= 1-70 A. Tolualdehydes : parameters as for benzaldehyde, with C--C(Me) = 132 A, C-H(Me)= 1.10 A and all Me angles tetrahedral, 1 Brown, Shoaf and Garg, Tetrahedron Letters, 1959, 3, 9. 2 Kahovec and Kohlrausch, 2. physik. Chem. By 1937,38,119. 3 Green, Spectrochim. Actrr, 1962,18, 39. 4 W e n , J. Chem. SOC., 1956,1350. 5 Wilmshurst and Bernstein, Cgn. J. Chem., 1957,35,911. 6 Green, Kynaston and Gebbfe, Spectrochim. Acta, 1963, 19, 807. 7 Pitzer, J. Chem. Physics, i946,14, 239. 8 Kilb, Lin and Wilson, J. Ckm. Physics, 1957,26, 1695. 9Packer and Vaughan, A Modern Approach to Organic Chemistry (Oxford University Press, 10 Fateley and Miller, Spectrochim. Acta, 1962, 17, 857. 11 Taimsalu and Wood, to be published. 1958), chap. 16.

ISSN:0014-7672    

DOI:10.1039/TF9646000005

出版商:RSC    

年代:1964

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No.13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions.Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Dielectric Relaxation Studies of Rotator Phase Solids Part 3.-Cyclohexane Derivatives BY GAYNOR ORF FIELD AND MANSEL DAVES The Edward Davies Chemical Laboratories, University College of Wales, Aberystwyth Received 11 th July, 1963 Dielectric measurements (E‘ and E”) have been made between 5 c/sec and 8-5 Gc/sec (1 = 3.4 cm) of solid, liquid and, in some cases, solution phases of cyclohexyl chloride, alcohol and ketone : cyclopentanol provides a refeience model having a more rigid ring.Equivalent d.c. conductances K are shown to provide (in addition to E’ and E”) excellent indications of phase changes. None of the dielectric absorptions measured arise from ring confornational changes. Cyclohexyl chloride and cyclohexanone behave dielectrically as rigid polar molecules having rotator phases. Cyclopentanol and cyclohexanol show, in the condensed phases, absorptions due to chain-associated hydroxyl groups. The small change in E’ at the f.p. for these compounds is the result of the hydroxyl group dominating the dielectric properties. Activation energies for the processes observed are discussed. Structures based upon cyclohexane are of interest owing to the variety of re- laxation processes which may arise.One characteristic feature is the chair-chair interconversion which, for a substituent X, represents an axial-equatorial inter- change (I). This interchange appears to involve an activation energy of -9-0 kcal/mole to first transform the chair into an energetically unstable boat-form.1 In principle this process should be detectable dielectrically as it involves a reorienta- tion of the (C-X) dipole. The claim has, in fact, been made that a low frequency absorption in cyclohexyl chloride and cyclohexanol arises from this source.2 The hydroxyl group in cyclohexanol introduces further possibilities. If ideally “ free ” it would contribute an absorption, probably in the microwave region (ca. 1012 clsec) corresponding to its own rotation about the (C-0) bond.3 Alter- natively, on the formation of hydrogen-bonded hydroxyl aggregates, characteristic of associated molecules, a co-operative reversal of (0-H) bond moments \ \ \ / / / S H .. . S H . . . 0-H+H-O.. . H-0.. . H-0 may occur: this is the origin of an absorption in long-chain alcohols studied by Meakins and Dryden.4 Finally, there will certainly be one v.h.f. absorption in the liquid and solution phases arising from the reorientation of the whole C6H11X molecule brought about by the permanent component moment tied to the cyclohexyl framework. There 10G. CORFIELD AND M. DAVIES 11 are indications that this " whole molecule " rotation can persist in the solid phase, at least near the melting-point, for some cyclohexyl derivatives.5 It was with a view to examining some of these features in typical structures that this dielectric study was undertaken.EXPERIMENTAL Both components of the complex permittivity, E' the real permittivity and E" the loss factor, have been measured at frequencies between 5 c/sec and 8 . 5 ~ lO9c/sec (A = 3.4 an). The whole of this range was used when satisfactory data over particular ranges were not available in the literature: no measurements have been made between 0.2 Mclsec and 250 Mclsec. For the range 5 c/sec to 160 kc/sec a direct-reading and caliiated version of the Thompson bridge,6 which could be balanced to 1 part in 104, was used in conjunction with a Hartshorn-Rushton 3-terminal e l l 7 housed in a Dewar flask (fO.5"C) within an earthed metal box. As a typical check we quote the E' values measured for chlorobenzene : at 20°, 5.71 (5-708) ; at -20°, 6.48 (6.45) ; at -47.2, 7*23(7.20).The best literature 8 values are in brackets. The methods at higher frequencies have already been described.9 EVALUATION OF DATA One important feature of the low-frequency measurements was the evaluation of the specific d.c. conductance of the medium. This follows from 1.80 x 1Ol2 li. f &"(total) = &"(dielectric) + &"(conductance) = E; + As E" is usually negligibly small below 1 kc/= or will increase proportionally to the fre- quency (fin c/sec) the best mean value of [&"(total) x f l as f+O gives IC, the specific conduc- ance (ohm-1 cm-1). In this way it is possible to determine ic to an accuracy of f l %, and usually free from polarization errors, for values from 1 x 10-4 to 1 x 10-14 ohm-1 cm-1. The presence of a single relaxation time z means adherence to the Debye equation (0 = 2'Tlf), (&& - &&)or 1+W2T2 ' &" = and the equivalent (Cole) forms, The latter provide good graphical methods of evaluating z.The more general condition involving a distribution of relaxation times has been represented by the Fuoss-Kirkwood 10 function : E' = &b - +.I&"); E' = &:, + (enjot). wheref, etc. represents the values at the peak of the loss curve. This can be evaluated forg via the first (adequate) approximation of taking the 1.h. bracketed term as unity and plotting cosh-1 (EL/&") againstf: correct choice of gives a line of slope 2.3038. The Debye case corresponds to /I = 1-00, and this factor is only rarely below 0.8; it can be converted to the Cole-Cole distribution parameter n via the equation, &/2 = n/cos (nzI4).For consistency in the comparison of energy and frequency terms, we have accepted the Eyring expression, z = - h exp g) exp (-:). kT (3) Thus log (Tz) has been plotted against (l/T) to obtain AH,12 DIELECTRIC RELAXATION STUDIES MATERIALS Cyclohexyl chloride was dried over CaS04, fractionated under reduced pressure (Van der Vloed 11) ; m.p. from cooling curve, -43.0"C (V. d. V. = -43.2'). Cyclopentanol was dried over CaSO4 and fractionated from a little sodium at 760 mm : b.p. 139*9-140.3"C ; m.p. from cooling curve, - 18.5rtl.O"C. Timmermans 12 gives b.p. 140*1'C, m.p. - 19-O"C. Cyclohexanol after standing over as04 was twice fractionally distilled from sodium : freezing commenced at 25.0" and was complete at 2403°C; Timmermans, 25.1OC.Other dielectric studies reported in the literature have been made on samples of m.p. 18-23', which indicates their water content : from the latent heat of fusion,l2 a m.p. depression of 1°C corresponds to 24mole solute per 1OOOmole of CyclohexanoL The small heat of fusion (0.43 kcal/mole) strongly suggests molecular rotation in the solid. Cyclohexanone was inadequately pudied by fractional distillation : it was separated from the bisdphite com- pound, dried (Na2SO4, m04) and twice fractionally distilled: freezing commenced at -30.1" and was complete at -31-3°C; Timmermans, -31.2. Cyclohexene was carefully dried and fractionally distilled. RESULTS AND DISCUSSION CYCLOHEXYL CHLORIDE White and Bishop,s and Crowe and Smyth 13 reported E' values at 50-100 kc/sec for the liquid and solid states from 90" to - 80°C : they gave no dispersion data but Reinisch 2 measured e' and E" from 80 clsec to 400 kclsec and from - 25' to - 65'C.Dieringer 2 and Kramer 14 have measured the microwave dielectric absorption in CC4 and c6H6 solutions of cyclohexyl chloride. The small change in E' at the f.p. indicates that the molecular reorientation is almost unhindered in the solid until the temperature falls to about -52°C when a sudden large decrease in d denotes transition to a rotationally frozen state. More unusual, however, is Mine. Reinisch's (and Dieringer's) claim that a very low- frequency absorption which she reports near -30°C in the liquid has its origin in an intra-molecular ring-flexing (chair-chair) process.2 An approximate activation energy of 16 kcal/mole quoted for this is not unreasonable compared with Reeves and Str$mme's 15 value of 10.8 kcal/mole for this interconversion as deduced from n.m.r.data for CS2 solutions of cyclohexyl chloride. Our observations consist of g' and E" values for solid and liquid cyclohexyl chloride from 5 c/sec to 150 kclsec and from 20" to -65°C. Fig. 1 shows the specific conductance of a sample as the temperature decreased. The m.p. (- 43°C) and a transition near -57°C are shown by the breaks in the plot. Written in the form IC = A exp (-E/l?T) the parameters are : liquid : A = 2.95 x €0-7 ohm-1 sec-1; E = 4.7 kcal/mole ; E = 15.6 ), solid I (to -57"), A = 6.6 x 103 Y, solid I1 (below -57"), A = 1 x 10-8 9 ) E = 4-0 ,) From both the IC and E' values, appreciable " super cooling" of about 2" (not well seen in fig.1) was found in the transition temperature: on reheating, little rotational melting could be detected below -52", but it was complete at -50°C. At frequencies below 50 kc/sec, E" (total) conformed precisely to a conductance term; i.e. at each temperature, for liquid or solid, fe"(tota1) was a constant to within &2 %. This suffices to establish the absence within this range of any di- electric absorption and Mme. Reinisch's claim cannot be confirmed: possibly her factor arose from electrode polarization effects.13 The permittivity values (fig.2) show good agreement between our own and Crowe and Smyth's data except in the evaluation of Ad = (Eiiquid-&,id) at the m.p. : G. CORFIELD AND M. DAVIES 2 0 . I . M$ Ttp. 3.4 3-8 4.2 4.6 7p. M.p. 1@/T FIG. 1.4ycIohexyI chloride : K = specific conductance ; T = OK. I I I I I I 1 I I V I 8 I their data suggest Ad = 1.0 ; our value is 1-5 3.0-2. However, the value 8' = 8.7 in the solid above -55" s 6 c e s to co&m molecular rotation in that phase. The14 DIELECTRIC RELAXATION STUDIES abrupt fall to 8' = 2.6 near -55°C gives a value for &&, i.e., for the permittivity in the absence of molecular rotation (ni = 2-14 at 20°C). It may be used in Onsager's equation to calculate the molecular dipole moment : for the liquid at 20°C, p = 2-0 D and there is no significant difference for the solid at -50°C.In dilute benzene solution p = 24D. Above 50 kc/sec, small but real values of dielectric loss could be detected in cyclohexyl chloride : from their proportionality to the frequency and eqn. (l), the order of magnitude of z could be estimated. For the solid at -55" (8' = 8-7; E;/'= 9 x lO-lO), z = 140 x 10-12 sec. These values conform to the " whole molecule " rotational pocess. Thus the dielectric behaviour of cyclohexyl chloride does not appear significantly to depart from that of a rigid molecule. CYCLOPENTANOL This compound has also been examined by White and Bishop 5 and Crowe and Smyth; 13 it shows behaviour in many ways similar to that of cyclohexanol. As the cyclopentyl ring is of a different flexibility, at least in amplitude, from the cyclo- hexyl ring, it provides a means of assessing any features in cyclo-hexanol which might arise from this flexibility.9.0 Y 0 g 9.4' -i 9-8 10.2 * 106. I I-O- I - 36 4.0 4.4 4-0 1031~ FIG. 3.-Cyclopentanol; K = specific conductance ; T = "K. 0 decreasingtemp.; ---- increasing temp. Solid, liquid and solution states have been studied from 20" to -75°C and from 5 clsec to 150 kc/sec. The specific conductance was accurately delineated by the E" values below 1 kcjsec and the IC values obtained on cooling the pure liquid and shown in fig. 3 are revealing. Supercooling of the liquid took place to about -23"G . CORFIELD AND M. DAVIES 15 and the first solid phase shows a transition near - 37", which is also clear from the E' values, which show a further transition at - 72°C.The conductance parameters are : liquid : A = 5-3 x 10-4 ohm-1 cm-1; E = 5-65 kcallmole ; solid I (to -37"), A = 1 . 6 ~ 1027 ,, ,, E = 40 7) solid II (to -72"), A = 2.4 x 10-2 ,, ,, E = 8.9 ,, As the second series of points in fig. 3 shows, the conductances were not quantita- tively reproduced on increasing the temperature : this is not surprising for the solid phases, but the same pattern of changes as on cooling is reproduced. At frequencies above 30 kcjsec at - 30" and of 300 c/sec at -70°C dielectric dispersion became very pronounced in the solid. This feature showed a slight departure from a single relaxation time and, for the evaluation of the main para- meters, it was adequately represented by the Fuoss-Kirkwood relations.The de- rived values of P for the absorption shows a slight temperature dependence being 3.8k0.2 at -20" and 4.9f0.2 at -70°C. These were quite consistent with the sudden fall of E' to 5.3 (at all frequencies up to 150 kclsec) with the second solid- phase transition at -72°C. Below that temperature (phase 111 solid), the dipole mobility giving rise to the absorption just discussed is clearly lost, so that the E' value should then correspond to E: for the absorbing phase. Fig. 4 and 5 summarize the principal features of this dielectric absorption. Fig. 4 shows the temperature variation of z : the line from - 37 to - 75°C gives, via eqn. (3), AH = 9.6 +Om4 kcal/mole : AS = 13.3 callmole deg. 2-6 30 3 4 n & M 3.0 3 1 v 4 -2 4.6 -0 -/: 0-1 4.1 4 3 4.5 4'7 49 1W/T FIG.4.Dielectric relaxation in solid cyclopentanol. 7 = relaxation time (sec) ; T = O K The transition at - 37" leads to no change in AH and amounts only to a shift of z by a frequency factor 1 - 6 k O . 2 , or 6(AS) = 0.91 cal/mole deg. Again, there is some difference in z between the cooling and heating sequences, but this likewise corres- ponds only to a small frequency-factor, despite appreciable differences in E' in the heating and cooling curves (fig. 5). The reproducibility of z and its A H emphasize that it is the same diRole process which is observed in the solid down to -72O. Fig. 5 shows the temperature and part of the frequency dependence of 8'. The m.p. is traversed with only a small change-an increase of 8.5 %, a value of the16 DIELECTRIC RELAXATION STUDIES same order as the molar volume change on freezing; cf.the following % decreases in volume on freezing ; CsH6, 11.4 ; C6H12, 5.3 ; C6B50B, 6.1. The transition temperature at -37" on cooling, however, brings about an increase of 30 % (33++ 435) in E' (at 10 kclsec). This confirms the large change in IC observed at this point. r 8 1: I,, ------;4 2nd. lr. p. Is%@ M.p, * - 00 - 6 0 -40 0 +2d t"C FIG. 5.-Permittivity of cyclopentanol as a function of decreasing and increasing temperature. frequency in had per sec: 103; 0 330; Q 100; -.- 33 krad/sec; 3-3 had/=. The further abrupt fall in E' to 5-3 on cooling through - 72°C has already been noted : by - 180"C, E' falls to 2.5 ; but, whilst the transition at - 72°C reappears on in- creasing the temperature, the transition is not to the phase I1 solid but to phase I.This is shown by the essential continuity of E' with the phase I values up to the m.p., i.e., the transition at -37" is not observed on reheating the phase I11 solid. Ac- cordinglyy we suggest that phase 11 is a metastable one. TABLE 1.DIELECIX.W ABSORPTION PARAMETERS FOR CYCLOPENTANOL IN t"C - 35.0 - 45.0 - 50.0 - 60.5 12.54 14.03 15.10 18.5 4.71 M p 3.0 3.0 3.1 3.1 1082 (Sec) 1.5 3.4 49 12.0 CYCLOHEXENE - 70.0 19.1 3.2 33 t"C -450 - 55.0 - 65.0 3.24 3.37 3-61 2.7 2.8 2.9 1082 (Sec) 0.67 1-40 3.30 Further evidence on the nature of the low-frequency absorption in cyclopentanol was sought from measurements up to 150 kclsec in cyclohexene solution. The solution absorptions had 8: values beyond 150 kc/sec ; thus at - 7O0CY E" (1 50 kclsec) was 4.24 for 4-71 M, whilst 8: = 8-0. Witbia these limits the absorptions conformed to eqn.(1) and were so evaluated. For 4.71 M, the values AH = 8.1 f0-6 kcall mole ; AS = 11.1 cal/mole deg. were found : for 1-34 M, AH = 7-3 4 1.0 kcal/mole ; A S = 10.2 callmole deg. The decrease in the AH frurn 9.6 kal/mole for the solid is not surprising. An even more marked influence is that of solvent dilution upon the peak absorption (c") :G . CORFIELD AND M. DAVIES 17 TABLE 2.-~~/[conc.] VALUES FOR CYCLOPENTANOL IN SOLID AND CYCLOHEXENE SOLUTIONS conc., M t°C -35.0 -45.0 -50.0 -55.0 -60-0 -65.0 11.0 (solid) 1-27 2.13 2-30 2.40 2.45 2-47 4.7 1 1 so2 1-17 1 -27 - 1.63 - 1.84 - 0.15 - 0.16 - 0.20 At 1.84 M the absorption is less than one-tenth the intensity expected on a pro- portional concentration basis from the solid.This adequately establishes that the absorption does not arise from any property of the individual cyclopentanol molecules but is a consequence of their interactions at higher concentrations, i.e., it arises from the hydrogen-bonded chain of hydroxyl groups whose presence has long been advanced as the origin of such absorptions in the solid phase alcohols.4 The comparatively high activation energy and high z values are due to the strength of the H-bond, entirely independent estimates of which in the solid and liquid alcohols 16 amount to 6.8 40.6 kcal/mole. The small change of 6' on freezing suggests a minimum dipole restriction in the solid phases I and I1 and White and Bishop discuss cyclopentanol under the heading " Molecular rotation in non-aromatic crystals ".However, the extensive H- bonding already present in the liquid and its increase in the solid is scarcely compat- ible with freedom of molecular reorientation in the latter. The explanation lies in the preponderance of the (0-H) group moment in the electric polarization of the alcohols. For an order-of-magnitude calculation we can represent the alcohol molecule as R-C-0-H, with L COH = 110" and the (0-H) group as the only non-rigid element : R R R c \ \ C \ 0-9D '\ C \ \ O-H---O-H---O-J-J--- 1-6 D ++ \ Using Smyth's bond moments,l7 the component moments perpendicular to and along the (C-0) axis are 1.6 cos 20°, and (0.9- 1.6 sin 20), i.e., 1.5 D and 0.36 D.The contributions of these independent items to the permittivity, i.e., to (6 -&A), or to the corresponding loss peaks &, are proportional to (mornent)z, i.e., the (0-H) rotation contributes ca. 94 % of the dipole polarization. Thus, although the liquid has already approached the molecular pattern of the solid, provided the (0-H) group can reorientate in the latter, €6 should not fall by more than ca. 6 % at the f.p. The fact that it increases is probably due to the increase in both the density and in the H-bonding in the solid. The above model is a gross simplification but one extension, due to Sack,ls in which allowance for the coupling of the (0-H) moments is made supports the conclusion, as n coupled dipoles have an effective moment which increases with n.This factor is the likely explanation of the further rise in 8'' on formation of phase I1 solid. The only plausible interpretation is that the (0-H) groups become more effectively linked-e.g., the chains become effectively longer-in phase 11. This fdvourable orientation does not appear to be readily attained as, once it is broken in passing to phase 111, it is not reformed without re-melting. The increased length of hydroxylic chains in phase I1 is also reflected in the marked decrease of activation energy for the d.c. conductance: they offer an easier channel for ionic charge transfer.18 DIELECTRIC RELAXATION STUDIES The role of the H-bond in determining the dielectric properties of cyclopentanol is seen if one uses Onsager's equation 19 to estimate (&+A) for the liquid : using the maximum plausible value p(CgH11OH) = 1.7 D, this factor becomes 5.9, which is approximately one-third of the observed value, (21 43 - 2.5) = 18.3.Sack's model would account for the observed value with n-4, a plausible figure for the mean degree of association. However, the alcohol behaviour is markedly determined by the energetics of the H-bond which greatly limits the applicability of Sack's model. Frohlich's relation,zO -E$C (l/kT) exp (+E/RT), assumes that the dipole occupies alternative orientations differing in energy by E callmole. The marked variation of 7%: for the phase I solid shows an appreciable value for E : the limited number of points give E = 4.0 kcal/mole. For phase I1 the TE:, values from -50 to -70°C are all 5.65+0.05 x 103, i.e., Ego.This differ- ence in E values conforms to the other features of phase I and phase I1 behaviour. Finally, there is one discrepancy to be mentioned. Our observation that et) falls only to 5-3 at -75", together with the similar values for e& above that tem- perature, implies that there is a further absorption in cyclopentanol, presumably at microwave frequencies. However, White and Bishop found E' = 2-7 just below -75", not very different from our e' = 2.5 at- 180" or ri: = 2-1. The retention of some phase I1 solid below -75" or some other non-equilibrium feature in our specimens could account for these results. CYCLOHEXANOL This compound was studied up to 10 Mc/sec by White and Morgan,21 Crowe and Smith,l3 and Meakins,22 whilst Arnoult et aZ.,23 and Mme.Reinisch,2 have reported measurements up to the micro-wave region. The reason for this interest is that the compound gives evidence of a rotator phase in the solid and it has a strong absorption ca. 105 clsec which Mme. Reinisch has ascribed to conformational (chair-chair) changes. Our measurements on solid cyclohexanol were from 5 c/sec to 150 kclsec, prin- cipally at - 10.0, - 30.0 and - 5O.O0C, and on solutions in cyclohexene over the kc/sec range and up to 900 Mclsec. From its f.p. (+24.8"C) we estimated our material to contain 7.3 moles H20 per 104 moles cyclohexanol: on cooling e' in- creased until it fell rapidly near - 60°C : on heating, it appeared that this was the result of much supercooling as transitions now occurred near -28" and -10°C.Reinisch reports the transition on heating at -9°C. Our data are summarized in fig. 6. Departures from a single Debye absorption (eqn. (1)) could not be detected : this was certainly so to within a few per cent for the solutions but it was only partially checked for the solid where &: was not measured. Our results for the solid agree well with Reinisch's, differing by a factor of ca. 1.6 from Meakins' values. The parameters of eqn. (3) are AH = 10.4+0.3 kcal/mole ; A S = 14.7 cal/mole deg., compared with AH = 9.6 kcallmole, AS = 13.3 cal/mole deg. for cyclopentanol. Fig. 6 also provides similar data over a wider temperature range for the 4.66 M solution in cyclohexene : AH = 10.2 TABLE 3.-vARIATION OF &k[COIlC.] WITH CONCENTRATION FOR CYCLOHEXANOL [conc]/toC 500 40.0 30.0 - 30 -40 969 M 0.475 0.537 0.60 0.95 1.01 4-66 M 0.247 0.288 0.326 0-97 1 -09 1-61 M - - - 0.27 0.28G.CORFIELD AND M. DAVIES 19 kcallmole ; A S = 22.2 cal/mole deg. For the 1-61 M solution AH = 10.0 kcal/ mole ; AS = 21-8 cal/mole deg. The relevance of the solution data is greatest in terms of ck/[conc.], shown in table 3 where the liquid phase values are from Reinisch.2 The pattern of behaviour of cyclopentanol is repeated here and the same con- clusions are drawn, i.e., the absorption is due to H-bonded hydroxyl groups. One difference is that on cooling cyclohexanol shows only the phase corresponding to phase I1 in cyclopentanol before transforming (supercooled) to phase 111 at -60". 1 0 3 1 ~ FIG. 6.-Dielectric relaxation times T of cyclohexanol ; loglo (TT) against 1W/T plots.Solid phase : 0 present data ; I_ Reinisch ; - - - - Meakins: scales top and right. 4-66 M solution in cyclohexene ; -I_ present data, scales bottom and left. The identification with phase I1 of cyclopentanol is made on the basis of the con- stancy of the factor T E ~ ; for cyclohexanol fron -25.0 to -60.0" it has the value 2-28 k0.06 x 103, i.e., the energy difference E = Oin Frohlich's equation. Accordingly, there is no qualitative difference between this absorption in cyclohexanol and the similar one in cyclopentanol and there is no support for the suggestion (Reinisch) that it arises from ring conformational changes. CYCLOHEXANONE White and Bishop5 and Crowe and Smyth 13 used only frequencies from 0-5 to I00 kc/sec ; Gautmann et al.measured E' up to 300 kc/sec for liquid and solid,24 and E' and E" for the liquid 25 from 1 to 250 Mc/sec; Dieringer measured cc14 solutions of cyclohexanone in the microwave region ; Reinisch 2 measured the solid from 80 c/sec to 12 kc/sec and Meakins 22 measured the liquid in the microwave region at one temperature and the solid from 1 kc/sec to 160 kc/sec, and at 1.1,20 DIELECTRIC RELAXATION STUDIES 3.1 and 8.4 Gc/sec at three temperatures. Calderwood and Smyth 26 measured the liquid at three microwave frequencies from 1 to 90°C. Apart from differences in detail, these results do not provide a direct comparison of the microwave loss processes in the liquid and solid phases and the marked low frequency absorption (8: at ca.100c/sec) found by Reinisch does not otherwise appear to have been investigated. 24.0 20.0 16.0 Eii 12.0- 8.0 - - - - I I I 1 I I I I I I t I I I Tr. p. M.p. -60 - 40 - 2 0 0 t"C FIG. 7.-Permittivity of cyclohexanone as a function of temperature. Y 3 I M 0 U 1 O3/T FIG. S.-Cyclohexanone : K = specific conductance : T = OK. Accordingly, measurements have been made on liquid and solid phases between 20 and -70°C (m.p. -30.7"C) over the frequency ranges 15 c/sec to 160 kc/sec and 250 to 8500 Mclsec. Some of the results are presented in fig. 7, 8, 9 and 10. The low frequency 4 values in fig. 7 show the small increase in permittivity at the21 f.p. : our values for the solid allow for a density increase relative to the liquid of 4 %: this factor appears to be neglected in other accounts. The solid phase transition often exhibited supercooling but on heating it occurred sharply at - 52.0 & 05°C.The supercooling is pronounced both for the freezing and subsequent G . CORFIELD AND M. DAVIES log10 0.J FIG. 9.--Solid cyclohexanone : electrode polarization process. w = frequency in radians per sec. 0 = at -69-7"C ; 7 at -63.2" (add 0.5 to log10 w scale values) I I I 3.2 3.6 4.0 4 -4 4.8 103/T FIG. 1O.Dielectric relaxation times for cyclohexanone. T = relaxation times in sec ; T = OK 0 present data ; i Caldenvood and Smyth data for liquid transition as shown in the log IC against 1/T plot (fig. 8) where the lines intersect at -47°C and - 57°C (cf. m.p. = - 30.7"C; t.p. = - 52°C). The conductivity of the cyclohexanone was much higher than that of the other compounds studied : a typical value was IC = 6-8 x 10-7 ohm-1 cm-1 at - 11°C ; cf.Gautmann et al. K = 30 x 10-7 ohm-1 cm-1 at - 10°C.22 DIELECTRIC RELAXATION STUDIES The plot in fig. 8 is based on a sample after exposure to a field of approximately lOOOV/cm for some hours. This treatment reduced the IC values uniformly by a factor of approximately 0.4. On average our liquid 86 values differ from Gautmann's and Calderwood and Smyth's by less than 1 %: there is similar agreement in the solid between Crowe and Smyth and ourselves except at - 60", below the transition : E ~ , C. and S. = 3-1 ; G. et al. = 2.67; present = 2-73. The value .$ = 2.73 is only attained at - 60" after cooling (- 8OoC) well below that temperature : otherwise there are varying amounts of the higher temperature phase present, giving E' values of 3.3 and more.The above 6 and IC values are based on measurements between 1 kc/sec and 1 60 kc/sec. Below that frequency, E' apparently increased with decreasing frequency, and fi", instead of remaining constant as a simple conductance function requires, showed a marked decrease. Taken together, these features indicate that electrode polarization effects are being observed. Of the various possible representations 27 that in fig. 9 shows log (C-Co) against logf, where C is the apparent capacitance and Co the value at frequencies sufficiently high to eliminate the polarization. The linearity of these plots conforms to Yager and Morgan's representation of electrode polarization effects.The theory of these feature has been developed : 28 our plots of capacitance and conductance against frequency have the same form as those given by Jaffi. Significantly, the electrode polarization features were the more pronounced the greater the K value deduced for the solid. Accordingly, we con- clude that the apparent absorption giving E" at 100 c/sec at -5O"C, and ascribed by Reinisch to conformational change in the cyclohexyl ring, is an artefact due to polarization at the electrodes. Both for the liquid (+25 to -25°C) and solid (- 30 to - 55°C) our measurements from 250 Mc/sec to 8500 Mc/sec showed only one absorption. Some difficulty was encountered at the highest frequencies (A = 3.4 cm); 8; values in excess of 6-0 accentuated the uncertainties already present from errors in estimating the depth and from fissuring of the cooled samples, and lead to irreproducibility in E' and E" to a maximum extent of 8 % for the solid.Both the liquid and solid absorptions showed slight but real departures from the Debye relations. The distribution of relaxation times was evaluated with the Fuoss-Kirkwood parameter p which approached the Debye value (p = 1) as the temperature fell : in the liquid, 0.80 ( +20°C), 0.82 (OO), 0.88 (-25") : in the solid, 0.87 (- 36"), 0.93 (-45°C). The associated z values have an uncertainty of + 5 %. From the log Tz plots (fig. 10) we deduce : for the liquid, AH = 2.25 kcal/mole ; A S = -0.9 cal/mole deg. for the solid, A H = 1-64 ,, ; A S = -3.4 ,, There is reasonable agreement with Calderwood and Smyth's data for the liquid; AH = 1-94 kcal/mole ; AS = - 1.7 cal/mole deg.; but there is a numerical error in Meakins' data which gives, for the solid : z( - 57°C) = 0.84 x 10-12 sec ; AH = 1.0 kcal/mo!e ; AS = +2-1 cal/mole deg. This discrepancy is also shown by a comparison of z values at 20°C for the liquid : in units of 10-12 sec these are 10.3 (Crowe and Smyth) ; 13-6 (Deiringer) ; 16-4 (Gautmann et al.) ; 0.69 (Meakins) ; 12.3 (present work). These data provide a picture of the dielectric polarization in cyclohexanone as due to a rigid dipole molecule suffering little restriction on its rotation in either liquid or solid states. From the 86 value for the liquid at 20"C, Onsager's equation gives p = 2-9 D, which compares with p = 2-80 D in dilute benzene solution.29 This agreement is maintained on going to the high-temperature solid phase andG.CORFIELD AND M. DAVIES 23 undoubtedly the latter is a " rotator-molecule " phase. Close similarities are found on comparison with the rotator phases studied by Clemett and Davies.9 Thus, AH(z) = 2.0 kcal/mole is significantly less than AH(q) = 2.85 kcal/mole for the liquid, evaluated from Calderwood and Smyth's viscosity data.26 This difference expresses the ease of molecular rotation for the quasi-spherical cyclohexanone molecule. It is this shape factor which promotes the high symmetry of the lattice formed at the f.p. Hassel and Sommerfield 5 found cyclohexanone to have a face- centred cubic lattice from -32 to -55°C and a non-cubic structure below -55" (cf.camphor and related compounds 30 which crystallize in a body-centred cubic lattice). As a consequence the solid rotator phase has an even lower energy for the dipole relaxation than the liquid : this is shown by the decreased slope in fig. 10 for the solid. The difference is not large but it is in the direction indicated, and represents the same conditions as in some other rotator phases9 It is the greater dissymmetry of the local field in the liquid which, despite the greater free volume in that state, produces a higher activation energy for molecular reorientation than in the solid. The rotational f.p. is at -52"C, as EI) there (2.74) is not markedly greater than = 2.10. Further, whilst there is good agreement between the E' values up to 160 kc/sec and those ca.300 Mc/sec (i.e., E; for the v.h.f. absorption) for the liquid, an appreci- able difference appears below the f.p. (-31°C) : TABLE 4.-PERMlTTIVITY OF CYCLOHEXANONE t"C 20.0 0 -25.0 -336.0 -45.0 -55.0 E' (up to 140 kc/sec) 16.1 rt0.l 17.4 f0.1 19.4f0-1 21.0 f0.2 22-3 f0-4 23.5 f0-5 E' (at 100 Mc/sec) 16-250.2 17.4 f0.2 19-0&0-3 18-6f0.4 18.7f0.4 18.4f0-4 Whilst formation of fissures such as occurs on freezing specimens in the coaxial line tends to reduce E'(obs.) below the correct value, the differences in table 4 are far greater than the likely error suggested by successive redeterminations. This feature, if real, should give rise to an absorption between 0.5 Mc/sec and 50 Mc/sec. White and Bishop 5 found a dispersion in the highly supercooled rotator phase having 7-8 x 10-7 sec at - 130°C.The absorption we have measured in the microwave region would have z = 5 x 10-10 sec at - 130°C. Gautmann et al. also indicate that they had some absorption in the solid (-32 to -55°C) with z ca. 10-8 sec. These features fit the observed difference in E', but more convincing loss measure- ments are needed to establish the z values. This absorption, if real, is confined to the solid state of cyclohexanone : there is no sign of it in the liquid. It could be that the greater part of the molecular reorientation in the solid takes place with the low relaxation time measured in the microwave region, some residual amount having a significantly larger z value. This could be the consequence of the energy variation being a function with three or more minima having different depths as the cyclohex- anone rotates in the solid. Correlation of the associated activation energies with the precise site-symmetry might be possible.CONCLUSIONS The results for the solid phases of cyclohexyl chloride and cyclohexanone appear to rule out the possibility of detecting dielectrically the conformational (chair-chair) changes in those particular structures. It is not expected that the conformational change should be observable in liquids or solutions as normally the " whole mole- cule" relaxation will occur there more rapidly than the chair-chair process. In24 DIELECTRIC RELAXATION STUDIES the solid phase, however, the latter might still be observable when the overall rota- tion of the polar cyclohexane derivatives is frozen. The present examples do not reveal this condition.Cyclopentanol and cyclohexanol are shown not to be rotator-phase solids as has been suggested, but to be dominated dielectrically by their hydroxyl groups whose ability to reorientate in the solid is associated with a significantly large activation energy. As has also been established by ultra-sonic studies,31 the activ- ation energy for the reorientation of these hydrogen-bonded groups is necessarily larger than the equjlibrium hydrogen-bond energy. The fact that such activation energies are fairly precisely measurable in the solid and that the influence of dilution and other lattice variables can be studied gives them much significance in assessing the role of the hydrogen bond in those circumstances. We thank the D.S.I.R. for a Research Studentship (G. C.). 1 Jensen et al., J. Amer. Chem. SOC., 1962, 84, 386. Moniz and Dixon, J. Amer. Chem. SOC., 2 Reinisch, Compt. rend., 1953,237,564 ; Thesis (University, Paris, Sorbonne, 1957). Dieringer, 3 Davies and Meakins, J. Chem. Physics, 1957, 26, 1584. 4 Meakins and Sack, Austral. J. Sci. Research, 1951, 4(2), 213. Meakins and Mulley, Austral. 5 Hassel and Sommerfeldt, 2. physik. Chem. B, 1938, 40, 391. White and Bishop, J. Amer. 6Thompsot-1, Proc. Inst. E.E. B, 1956, 103, (12), 704. 7 Hartshorn and Rushton, Proc. Insi. E.E., 1953,100,94. 8 Maryott and Smith, Nat. Bur. Stand. circ. 514, 1951. 9 (a) William$, J. Physic. Chem., 1959, 63, 531. (b) Clemett and Davies, Trans. Faraday SOC., 10 Fuoss and Kirkwood, J. Amer. Chem. SOC., 1941, 63, 385. 11 Van der Vloed, Bull. SOC. Chim. Belg., 1939,48,229. 12 Timmermans, Les Constantes Physiques des Composis Organiques Crystallisb (Mason et Cie, 13 Crowe and Smyth, J. Amer. Chem. SOC., 1951, 73, 5406. 14 Kramer, Z. Naturforsch., 1960, 15, 552. 15 Reeves and Str~mme, Can. J. Chem., 1960, 38, 1241. 16 Davies and Kybett, Nature, 1963, 200, 776. 17 Smyth, Dielectric Behauiour and Structure (McGraw-Hill, New York, 1955). 18 Sack, Austral J. Sci. Research, 1952, 5(1), 135. 19Onsager, J . Amer. Chem. SOC., 1936, $8, 1486. 20 Frohlich, Theory of Dielectrics (Oxford University Press, 1949). 21 White and Morgan, J. Amer. Chem. SOC., 1935, 57, 2071. 22 Meakins, Trans. Faraday SOC., 1962, 58, 1962. 23 Arnoult, Lebrun and Boullet, Arch. Sci., 1956, 9, 44. 24 Gautmann et al., Helv. chim. Ada, 1956, 39, 132. 25 Gautmanu et af., Helv. chim. Acta, 1956, 39, 145. 26 Calderwood and Smyth, J. Amer. Chem. Soc., 1956,78, 1295. 27 Yager and Morgan, J. Physic. Chem., 1931, 35,2039 ; see also Murphy and Lowry, J. Physic. 28 Jaffk, Physic. Rev., 1952, 85, 354. 29 Landolt-Bornstein, 6te Auflage, 1 Band, 3 Teil (Springer, Berlin, 1951). 30 Finbak, Arch. Math Naturvidenskab, B, 1938, 42, 77. 31 Maier, Sociktt? Chim. Physique, Symposium (Paris, June, 1963). 1961, 83, 1671. Harris and Sheppard, Proc. Chem. SOC., 1961, 418. Z. Physik, 1956, 145, 185. J. Sci. Research, 1951, 4(3), 365. Dryden, Austral. J. Sci. Research, 1952, 5(4), 661. Chem. SOC., 1940, 62, 8. 1962, 58, 1705, 1718. Paris, 1953). Chem., 1930,34, 598. Macdonald, Physic. Rev., 1953, 92, 4.

ISSN:0014-7672    

DOI:10.1039/TF9646000010

出版商:RSC    

年代:1964

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Pre-Freezing Phenomena in Relation to Liquid-Crystal Formation BY E. MCLAUGHLIN, M. A. SHAKESPEARE AND A. R. UBBELOHDE Dept .of Chemical Engineering and Chemical Technology, Imperial College, London, S.W.7 Received 26th July, 1963 Measurements of viscosity have been made on the nematic and isotropic forms of p-azoxyanisole and on mixtures with phenanthrene added to depress the freezing and transition points. Dilato- metric measurements on pure p-azoxyanisole have also been made. New studies of the phase diagram of the pure compound and of its mixtures with phenanthrene confirm the existence of a region with two liquid phases. Transport mechanisms are discussed for both isotropic and nematic liquids. In studying the inter-relations between transport mechanisms and liquid struc- tures it can be informative to examine systems in which the same molecules are arranged in more than one structure.One important class of systems comprises liquid crystals. p-Azoxyanisole which provides a well-known example of a liquid crystal whose nematic range extends from 118.2 to 1353°C was chosen for the present work. Various investigations 1 point to the presence of oriented swarms or bundles which from dielectric measurements are estimated to contain about 104-105 molecules. Long axes of these molecules are parallel but are not arranged in layers. Near the melting point such bundles are probably hundreds of times larger than the interlocking clusters whose presence has been inferred in melts of various non-spherical molecules, from the behaviour of the transport properties as the freezing point is approached and traversed.2 This makes it interesting to compare the effects of such larger molecular assemblies on the viscosity near the freezing point.Mixtures of p-azoxyanisole with phenanthrene were also included in the present investigation, since this impurity might affect transport properties differently in the nematic and isotropic liquids. EXPERIMENTAL p-Azoxyanisole was recrystallized from benzene and heated near to its melting-point (1 18-2°C) in vacuo to remove retained solvent. Phenanthrene (m.p. 99~1°C) was purified by recrystallization and chromatography with benzene on a column of alumina. It was then sublimed in vacuo to remove retained solvent. Mixtures of the two components were prepared by sealing weighed amounts in Pyrex tubes and heating to about 150°C, with constant shaking. Techniques for dilatometry and for the determination of viscosity have been previously described.3 The viscosity measurements, which were made at flow rates from about 0.05 to 0-15 ml min-1 in a 0.2 mm bore capillary, did not exhibit any non- Newtonian effects such as were reported by Peter and Peters 4 at lower shear rates (cf.also Ostwald 13). Phase changes for the various compositions with phenanthrene were observed with the mixtures by noting the temperature at which phase separation occurred in the viscometer. Fig. 1 records changes of volume with temperature. Precise values of molar volumes at the melting point Tf and the clearing point Tc are given in table 1. Premonitory effects are found over a range of temperatures before the actual transitions, as illustrated in fig. 1. 2526 LIQUID-CRYSTALS Clearing occurs over a narrow range of temperatures.In table 1, the value of Yfliquid) for the anisotropic liquid at Tc was obtained by straight-line extrapolation of data for pure parazoxyanisole from T,- and does not include the small enhanced increase in the pretransi- tion region, indicated in fig. 1. Densities of the nematic phase agree within experimental error (f0.01 %) with those of Maier.5 T"C FIG. 1 .-Molar volume/temperature behaviour of pure p-azoxyanisole. With added phenanthrene, the phase diagram derived from the present observations is recorded in fig. 2. This molecule was chosen as impurity because it is rigid and is ob- tainable in the pure state; its dilatometric behaviour has also been studied in the pure melt.6 The two liquid phases became readily apparent during viscosity measurements.TABLE 1 .-VOLUME PARAMETERS FOR p-AZOXYANISOLE (ml/mole) Ty "C Tc°C V, solid 199.35 V, liquid anisutropic 225-04 V, liquid anisotropic 22 1.34 V, liquid isotropic 225.86 100 A yfl V, 11.03 * 100 AVJV, 0.36 * to a clear liquid. * 100 A Vf/ V, and 100 A V,/V1 are the respective % volume changes on fusion and on transition In the region of concentrations from 0-8 % phenanthrene the mixtures separated into lighter (clear) and denser (opalescent) phases. A similar two-phase liquid region has been reported for additions of up to 10 moles % of hydroquinone to p-azoxyanisole.7 Effective viscosity measurements could not be made when two liquid phases were present; this is indicated by the broken lines in the viscosity plots recorded in fig.3. Although Dave and Dewar 8 did not observe any separation into two liquid phases, their results regarded as mean values agree well with the phase diagram in fig. 2. The present viscosity results (accurate toE. MCLAUGHLIN, M. A . SHAKESPEARE AND A . R. UBBELOHDE moles % p-azoxyanisob FIG. 2.-Phase diagram of the p-azoxyanisoIe+ phenanthrene system. 0, present work; a, Dave and Dewar. 1.52 - n m .I 0 1.48- a 4 W E 8 1.44- 4 1-40- 1.36 I 27 I 1 23.2 24.0 2 5 . 0 26.C ’ _ ~/T”K x 104 FIG. 3.-Viscosity/temperature behaviour of the system p-azoxyanisole + phenanthrene at low concentrations of phenanthrene. 0. 100 %; 0,99.15 %; El, 97-16 %; 0-, 95.21 %; p-azoxyanisole.28 LIQUID CRYSTALS f0.005 cp) and those of Peter and Peters for high shear rates, given below for three tem- peratures, can be seen to be in good agreement. For the isotropic liquids, viscosities could be measured over a considerably wider range of temperatures and concentrations than for the nematic phase.Results are recorded in fig. 4. l/T°K X 104 FIG. 4.-Viscosity/temperature behaviour of the system p-azoxyanisole+ phenanthrene at higher phenanthrene concentrations. 0 , O %; 6, 13.33%; 0 , 2 8 * 9 5 %; 0 , 58-25 %; b, 83.23 %; El, 93-13 %; and 0, 100 % I p-azoxy anisole. DISCUSSION Table 1 shows that the volume change on melting p-azoxyanisole is about 30 times larger than the volume change at the clearing point. Molecular rearrangements to form the isotropic phase at the clearing point thus involve only minor increases of volume.TABLE 2.-cOMPARISON OF VISCOSITY MEASUREMENTS (viscosities in centipoise) temp., O C ref. (3) temp. "C present work 119 2.58 1 19.0 2.587 125 2.43 125-2 2435 131 2.36 130.4 2-361 For p-azoxyanisole, no direct calorimetric observations appear to have been made of the heats of fusion, and of transition to a clear liquid. If the narrow region where phase separation occurs (inset in fig. 2) is neglected, the phase diagram with phenanthrene (fig. 2) yields approximate values for heats of melting and clearing of 6.9 and 1.3 kcal mole-1 respectively, with corresponding entropies of 17-7 and 3.2 cal deg.-1 mole-1. These figures are obtained assuming that conventional thermodynamic equations may be applied toE. MCLAUGHLIN, M . A . SHAKESPEARE AND A .R. UBBELOHDE 29 calculate depression of freezing point or clearing point respectively, and that the phen- anthrene impurity is soluble to any appreciable extent only in the isotropic liquid. While these values must be treated with reserve they indicate that most of the disorder in passing from the solid to isotropic liquid occurs at the melting point rather than the clearing point in agreement with the conclusions from the volume changes. It has been suggested (e.g. ref. (1)) that the increase of disorder on melting includes rotational motion about the long axis of p-azoxyanisole. To test this hypothesis, the volume required for free rotation has been estimated using the method previously described2 The repulsion envelope for p-azoxyanisole was calculated on the basis of the known struc- ture of azobenzene. It was found that about 400ml/mole are required for complete rotational freedom about the long axis, i.e., about twice the volume actually occupied in liquid anisotropic p-azoxyanisole, extrapolated back to the melting point.Although the orientation of the dipoles in this molecule must undergo increased randomization on melting, the conclusion is that there is on average no room for the molecules to rotate freely about their long-axis, either in the anisotropic or isotropic regions. T T FIG. 5.-The degree of order S as a function of temperature for p-azoxyanisole (copied from Weber). 0, 0, magnetic resonance methods ; x , 0, optical methods ; ., diamagnetic methods. Some forms of randomization of molecular arrangement must, however, occur both at the melting and at the clearing points, to account for the entropy changes, and the destruction of optical anisotropy.These seem likely to involve some randomization of orientations about axes perpendicular to the long axis of the molecules, as suggested by Chatelain.9 As a working model of the liquid crystal phase it is therefore assumed that bundles of about 104 ordered molecules (cf. dielectric measurements) exist in a matrix of disordered molecules which correspond with the normal isotropic liquid. Within a bundle, however, the molecules need not all be completely aligned ; similarly, in the isotropic fluid, parallelism may occur between much smaller groups of molecules. The latter small groups have been called by Stewart 10 cybotactic clusters.An overall degree of order S of the liquid-crystal phase may be defined by the relation s = +( 3 cos2 8 - l)avm,30 LIQUID CRYSTALS where 8 is the angle between the molecular axis of greatest polarizability and the optic axis of the liquid crystal. The overall degree of order defined in this way makes no dis- crimination for micro-deviations from complete order within a bundle, and complete dis- order within the isotropic liquid. Experimentally, this degree of order in the nematic phase has been measured by various techniques.11 Fig. 5 records the results; the solid curve is used in discussing what follows. INTERPRETATION OF THE VISCOSITIES In the isotropic liquid (to the left of fig. 3) a normal exponential relationship is found for the dependence of viscous flow upon temperature For the pure melt, the line of closest fit calculated for the logarithmic plot corresponds with qo = 4 .5 5 ~ 10-2 millipoise ; E, = 5300 &/mole. Results show that values of the activation energy E,, are not sensitive to the admixture with phenanthrene. When the portions of fig. 3 and 4 exhibiting the normal behaviour of a polar liquid are represented in terms of the empirical mixture law previously put forward 12 where y11 and 492 are respective viscosities of pure phenanthrene and p-azoxyanisole, and x is the mole fraction of phenanthrene, the cross-term q12 fits fairly well with the arithmetic mean y12 = (4yl+yl22)/2 as is illustrated by table 2. These findings suggest that momentum transfer and molecular movement are linked in the normal way in the isotropic liquid and in its mixtures with phenanthrene.TABLE 3 . 4 ~ 0 s s - m ~ ~ COEFFICIENTS 1112 (millipoise) IN mscosm OF - x T"C 120 130 140 150 160 181.5 0.133 28.48 * 24-29 * 20.87 18.44 16.32 13-43 0.289 28.18 * 23.97" 20.63 18.15 16.06 13-55 0.583 27-69 * 23.91 * 19.36 17.01 16-05 13.21 0.832 30.28 * 24*32* 20.14 18.39 17.67 14.75 average 28.66 24.12 20.25 18.12 16-53 13.73 arithmetic mean 27.99 23.70 20-30 17-43 15-25 12.03 geometric mean 2458 21.09 18.27 15.90 14.09 10.97 * based on extrapolated values for the viscosity of isotropic p-azoxyanisole. In the anisotropic region, fig. 3 points to a different temperature dependence. With pure p-azoxyanisole, the viscosity at first decreases through a minimum and then rises steeply to a high value for the isotropic liquid.For the pure melt, minimum viscosity is found at 130*4"C, about 5°C below the clearing point and hence well away from the region (cf. fig. 1) where the volume rises most steeply from the anisotropic to isotropic liquid phase. As a working hypothesis, when a shear stress is applied to the liquid as a whole, it may be assumed that relaxation during times characteristic of viscous flow in the present experi- ments can be neglected within a bundle, compared with relaxation in the isotropic regions surrounding it. Motion in isotropic regions will to a first approximation be governed by the same mechanism and the same flow parameters (eqn. (l)), as when the liquid is wholly isotropic. On this basis, a molecule must be outside a swarm before it can contribute to the momentum transfer underlying the viscosity.This hypothesis leads to an additional pre-exponential factor in the temperature dependence of viscosity. The presence of aniso- tropic bundles confers a degree of order S on the liquid as a whole, as discussed above. If disordered regions are a prerequisite for momentum transfer, at any temperature Ti eqn. (1) when applied to the anisotropic liquid must be multiplied by (1-&) the degree ofE. MCLAUGHLIN, M. A. SHAKESPEARE AND A . R. UBBELOHDE 31 disorder. Unlike qo this factor is temperature dependent. In the simplest statistical theories of ordering, as, e.g., in that of Bragg and Williams, Sj becomes zero and this factor becomes unity for Z>T,.In addition, the bundles also cause an increase of vis- cosity by acting as colloidal particles according to the Einstein equation, which, modified for higher concentrations, may be written 2 for any constant Tj in the form v = rlo ~ X P (EqiRT,>[1+ a#i + P421 (3) where # j is the volume fraction of liquid present as bundles. Eqn. (3) is valid for volume fractions of spherical particles up to about 30 % with the constants u and /3 taking values 2.5 and 7 respectively. Bundles are more likely to behave as ellipsoids but this does not greatly change the numerical factors in (3) unless the axial ratios difYer greatly from unity. On this basis the equation for the viscosity of the nematic liquid may be written 11 = (1-si)ro exp ( E ~ / R T , > [ ~ +~4i+842], (4) where # j and Sj are temperature dependent quantities.The combination of the (1-Sj) and exponential curves serve to produce the characteristic viscosity curve of fig. 3 for the nematic phase. An algebraic form of Si as a function of Tfor the nematic phase has been proposed by Weber.11 With the values of Si at various temperatures taken from fig. 5 and using qo and Eq from eqn. (I), eqn. (4) has been solved for # i using measured values of qi at the various temperatures c. Results calculated on this basis are recorded in fig. 6, and show that T T FIG. 6.-The volume fraction of clusters $ j in the nematic phase. 4j falls steadily from the melting point to the clearing temperature at which it suddenly drops to zero. In conjunction with the entropy and volume data the small values of $ j suggest that in the liquid crystal phase the fraction of molecules sequestered within bundles is small. The sensitivity of viscosity to the presence of foreign molecules is different for the two different liquid structures. As can be seen from fig. 3 and 4, the viscosity in the isotropic phase is relatively insensitive to small additions of phenanthrene. A much more pro- nounced effect is, however, found for small additions of phenanthrene in the nematic phase. Part of this influence of impurities arises from the thermodynamic depression32 LIQUID-CRYSTALS of the clearing point Tc due to their presence. Conceivably, they may also affect the degree of order in the liquid structure, in other ways; such possibilities cannot, however, be tested until independent methods of evaluation cf liquid structure can be used to interpret the curves for Si recorded in fig. 5. 1 Brown and Shaw, Chem. Reu., 1957, 57,1049. 2 McLaughlin and Ubbelohde, Trans. Faraday SOC., 1958, 54, 1804. 3 Andrews and Ubbelohde, Proc. Roy. Soc. A, 1955,288,435. 4 Peter and Peters, 2. physik. Chem., 1955, 3, 103. 5 Maier and Saupe, 2. Nuturforsch., 1960, 15a, 287. 6 Al Mahdi and Ubbelohde, Proc. Roy. SOC. A, 1953,222,195. 7 de Kock, 2. physik. Chem., 1904, 48,129. 8 Dave and Dewar, J. Chem. SOC., 1954, 4616. 9 Chatelain, Bull. SOC. Franc. Min., 1955, 78,262. 10 Stewart, Physic Rev., 1927, 30, 232. 11 Weber, Disc. Furaday Soc., 1958, 25,77. 12 Hind, McLaughlin and Ubbelohde, Trans. Faruday SOC., 1960, 56, 328. 13 Ostwald, Truns. Furaduy SOC., 1933, 29, 1002.

ISSN:0014-7672    

DOI:10.1039/TF9646000025

出版商:RSC    

年代:1964

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Self-Diffusion in Mixtures Part 6.-Self-Diffusion of Hydrogen in Certain Gaseous Mixtures BY L. MILLER AND P. C. CARMAN National Chemical Research Laboratory, South African Council for Scientific and Industrial Research, Pretoria, South Africa Received 8th October, 1963 Tritium has been employed as an isotopic tracer to determine self-diffusion of hydrogen in admixture with C02, CF2C12, krypton and xenon. Owing to the large difference in mass between HT and H2, tracer diffusion of tritium is not directly related to self-diffusion of hydrogen, and a brief theoretical exposition of their relationship is given. In part 41 the self-diffusion of heavy gases in admixture with hydrogen was reported. Completion of the investigation by measurement of self-diffusion of hydrogen in the same mixtures is now presented.The original intention to use ortho- and para-hydrogen had to be abandoned, as liquid hydrogen was not avail- able, so that diffusion of tritium has been followed, together with corrections for its mass. EXPERIMENTAL GASES Purified xenon and krypton were purchased and used without further purification. Commercial freon-12 was fractionally distilled, and hydrogen was subjected to the usual methods of purification. Tritium was purchased from the Radiochemical Centre, Amersham, and, to ensure that it was converted entirely to HT molecules, it was mixed with excess hydrogen and circulated for about 30min over a bright hot platinum wire.2 APPARATUS A N D PROCEDURE An ionization chamber of Borkowski type 3 was used in connection with a vacuum apparatus as described in part 4.The ionization chamber was the bottom cell of a vertically designed Ney-Armistead4 diffusion apparatus, kept at 20°C in an air thermostat. The change of the ionization current was observed by reading the voltage at the ends of a resistor of 5 x 1010 ohms with a Vibron Electrometer model 33C, manufactured by Electronic Instruments Ltd., Richmond, Surrey. The radioactivity used was high enough to work in the highest range (1000 mV) which was not very sensitive to disturbances. The flow of air through the thermostat was such that a small temperature gradient existed from bottom to top and so stabilized the system against convec- tion.At the end of the experiment, the gradient could be inverted to promote convection and so speed up the approach to homogeneity. The apparatus constant was not calculated from the geometry (Vl = Y ionization chamber = 293 ml, V2 = 437 ml, connection tube length L = 16 cm, area A = 0-25 cm2) but by measurement of interdiffusion in the system H2-HT. If hydrogen 2 3334 SELF-DIFFUSION I N MIXTURES isotopes are assumed identical in diffusive properties except for mass, this should be equal to the interdiffusion coefficient for H2-D2, as determined by Bendt,s and to the mass-corrected value for orthohydrogen-parahydrogen , as determined by Harteck and Schmidt.6 The values given by these two investigations agree well and lead to a value of 1.25 cm2/sec at 20°C for H2-D2 or for H2-HT.From viscosity measurements, however, Weissman and Mason 7 deduce that the value for H2-Dz should be 1-22 cmalsec. The apparatus constant obtained from the former value was checked by measurement of self-diffusion of C02, using C14O2, and of krypton, using Kr85, with the results in table 1. The agreement is satisfactory if special weight is given to the more recent determinations of Schafer and co-workers, and if 1.25 cm2/sec is accepted as the correct value for H2-HT. TABLE ~.-SELF-DIFFUSXON COEFFICIENTS FOR C02 AND FOR Kr AT 20°C IN cm2/sec Data of Amdur and of Winter temperature-corrected with exponent n = 1.934 Amdur et aZ.8 0.1 11 Groth and Harteck 11 0,093 Winter 9 0.1 10 Schafer and Schuhmann 12 0.0895 Schafer and Reinhard 10 this work 0.107 this work 0.0905 COZ Kr 0- 1075 Preparation of mixtures and measurements of tritium diffusion were in accord with the procedures in part 4.1 Normally, tritium diffusion took place from the bottom cell (ionization chamber) towards a mixture containing the same percentage of heavy gas.When the percentage of heavy gas was over 99%, however, the same result within experimental error was obtained by diffusing into 100 % heavy gas. THEORY In this system, H2 is labelled with HT, which has twice the molecular weight, so that results must be interpreted as diffusion of HT in a ternary system. The sub- scripts 1, 2, 3 will denote H2, heavy gas and HT, respectively. Then, if 216 denotes diffusive velocity, Nf mole fraction of component i, we measure the experimental a a a diffusion coefficient of HT, D:, where using VN3 for (% + au + -) N3, 82 Now, in a ternary system,l3 N l N , N2N3 D13 D2 3 -VN3 = ----(v3 - Vl) + -(v3 - vz), (3) together with a third equation for -VN2 which need not be written down, since and hence (4) (5) The experiment is carried out under constant pressure conditions so that there is no net flow of volume, whence o,N1+ uzN2 + ~ 3 N 3 = 0.(6)L. MILLER AND P . C. CARMAN 35 In our case, it is arranged that whence By applying (6) and (8) to (2) and (3), VN1, 01 and 212 can be eliminated, leaving VN2 = 0, (7) VN1 +VN3 = 0. (8) Furthermore, since tritium was used only in trace quantities, and Applied to (9), this leads to N,=0, N1+ N2- 1. (10) VN3 N , N2 - --- --+-.I -- D3 v3N3 a,, D23 Since the binary interdiffusion coefficients, 0 1 3 and D23 are, to a first approximation, independent of composition, then a plot of the reciprocal of the experimental dif- fusion coefficient for tritium is a linear function of the mole fraction of the heavy gas. No limitations are placed upon the molecular weight of HT. Eqn. (11) would be equally applicable if a labelled molecule identical in molecular weight to H2 were employed, in which case it would become which is the exact analogue of the case discussed in part 4. The binary coefficient D13 is simply related to the self-diffusion coefficient for hydrogen D11, since we can assume that HT is identical with H2 in all diffusive properties except mass. It thus follows that - Ml +Ml - M , = D,,$.M 1 + M 3 M l The soundness of this calculation is shown by agreement of Dll for H2 obtained from measurements of Bendt and of Harteck and Schmidt. By similar reasoning, Dz3 is related to the binary coefficient D12 by RESULTS Measurements were made at pressures ranging from 50 to 4-00 mm, but the pressure corrected diffusion coefficients did not show any effect from this. The systems examined were the three in part 4, i.e., admixtures with COa, Kr and CF2C12, and also the Hz-Xe system. The data obtained are plotted in fig. 1 as reciprocals of the experimental diffusion coefficients for tritium against the mole fraction of the heavy gas. In each case, the data conform substantially to straight lines. At36 SELF-DIFFUSION I N MIXTURES the one end is the reciprocal of the coefficient, D13 = 1-25 cmz/sec, which was used for calibration of the apparatus. At the other end are values of 0 2 3 and the cor- responding values of D12 are known from the literature.The data of Schafer, Corte and Moesta 14 give 0 1 2 = 0.675 cm2/sec for hydrogen-poor mixtures, whereas the value given here is 0.473 x J(2 x 46/48) = 0.656. In part 4, our values for H2-Kr and for H2-CF2C12 at the hydrogen-poor end were 0.710 and 0.392, respectively, which compare well with the values given here of 030 x J(2 x 86/88) = 0.70, and of 0-290 x J(2 x 1231125) = 0406. P 3 3 r N2 I_ 05 N2 FIG. 1. For H2--Xe, the only published result for interdiffusion is that of Paul and Srivastava,15 the interpolated value at 20°C being 0.57 cm2/sec whereas our value for the hydrogen-poor end is 0-444 x J(2 x 133/135) = 0.624 cmZ/sec.This is about 9 % higher, but Paul and Srivastava carried out diffusion between the two pure gases, so they would obtain an average for the whole composition range. Together with experimental errors, this can perhaps account for the difference. Thus, for H2-CO2, the value for the hydrogen-rich end is 0.597 cm2/sec, and for an equi- molar mixture is 0-622 cm2/sec, i.e., there is a sharp upturn to 0-675 cm2/sec at the hydrogen-poor end. It has not been considered of sufficient interest to calculate and present values for self-diffusion coefficients of hydrogen in the mixtures, 0;. There is no wayL. MILLER AND P . C. CARMAN 37 of making mass-corrections to convert experimental values of 0; to corresponding values of 0:. From eqn. (12), (13) and (14), however, 0: can be calculated using values of D13 and 0 2 3 obtained in the experiments, since This paper is published by the permission of the South African Council for Scientific and Industrial Research. 1 Miller and Carman, Trans. Faraddy SOC., 1961, 57,2143. 2 Schirdewahn, Klemm and Waldmann, 2. Naturforsch., 1961, 16a, 136. 3 Brownell and Lockhart, Nucleonics, 1952, 10,29. 4 Ney and Armistead, Physic. Rev., 1947, 71, 14. 5 Bendt, Physic. Rev., 1958, 110, 85. 6 Harteck and Schmidt, 2. physik. Chem. B, 1933, 21, 447. 7 Weissman and Mason, J. Chem. Physics, 1962, 37, 1289. 8 Amdur, Irvine, Mason and Ross, J. Chem. Physics, 1952, 20,436. 9 Winter, Trans. Favaday Soc., 1951,47, 342. 10 Schser and Reinhard, 2. Naturforsch., 1963, 18a, 187. 11 Groth and Harteck, 2. Elektrochem., 1941, 47: 167. 12 Schafer and Schuhmann, 2. Elekfrochem., 1957, 61,251. 13 Curtiss and Hirschfelder, J. Chem. Physics, 1949, 17, 550. 14 Schafer, Corte and Moesta, 2. Elektruchem., 1951, 55, 662. 15 Paul and Srivastava, J. Chem. Physics, 1961, 35, 1621.

ISSN:0014-7672    

DOI:10.1039/TF9646000033

出版商:RSC    

年代:1964

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Translational Thermal Conductivity and Viscosity of Multicomponent Gas Mixtures BY R. s. GAMBHIR AND s. c. SAXENA Physics Dept., Rajasthan University, Jaipur, India Received 29th May, 1963 The Chapman-Enskog expressions for the translational thermal conductivity hmix and viscosity v d x of a binary gas mixture have been transformed into the following form suggested by Sutherland and Wassiljewa : The temperature and composition dependences of the constants +Q have been investigated.A general relation giving the ratio 412/421 is derived. It is also possible to obtain explicit expressions for +Q for a particular type of binary mixture, viz. where the mass of one component is far greater than that of the other. These expressions do not involve terms requiring a knowledge of inter- molecular forces. Various workers while dealing with the translational thermal conductivity Amir and viscosity qm of an n-component gas mixture have found the expression, to be useful. In eqn. (l), Ai, qi, and Xi denote the thermal conductivity, viscosity and mole fraction of the ith component, respectively.We will consistently use the subscript i for the heavier component. The preference for the form of eqn. (1) is three-fold: (i) for correlating the data over the entire composition range; (ii) for predicting the mixture properties at high temperatures from the knowledge of pure gas properties only, and (iii) for evaluating the multicomponent properties with the use of related binaries only. There are also three different ways in which eqn. (1) has been used depending upon the particular procedure adopted for computing &. These are : (i) APPROXIMATE METHOD, where an approximate relation is used for computing 4ij.1-6 (ii) SEMI-EMPIRICAL METHOD, which employs a semi-empirical relation for the ratio &/t$ji, and one Amix or q m h value to compute q5cj and 432.One such relation was suggested by Mason and von Ubisch.7 Another relation was suggested by Wright and Gray 8-11 (iii) EMPIRICAL METHOD, where 48, and 4 j i are treated as disposable parameters and are evaluated from the knowledge of A m ~ or q m h values at two compositions.12-16 it is of interest if more rigorous expressions under well-defined approximations may be derived for them. One method starts from the rigorous Chapman-Enskog expression for Amh or qmix and then trans- forms it into the form of eqn. (l).49 6917 Wright and Gray 8 have suggested a com- paratively rigorous method for a binary system. We will extend their 8 work to get explicit expressions for 4 ~ . These expressions may also lead some support for the various empirical a d semi-empirical computational procedures.In view of the varied usefulness of 38R. S. GAMBHIR AND S. C . SAXENA 39 RIGOROUS EXPRESSIONS FOR 4ij AND (bjl The rigorous expression of Muckenfuss and Curtiss18 for Amix of a two-com- ponent gas system, as modified by Mason and Saxena,lg can be written as 16T 2 5 P 16T fl=- 25P 16T y=- 2 5 P a=- and I Here, M represents the molecular weight, D 1 2 the mutual diffusion coefficient of components 1 and 2 in cm2sec-1, Ain ergcm-1 sec-1 deg.-1, p the pressure in dyne cm-2, T the temperature in 0°K and the remaining quantities are as defined by Hirschfelder, Curtiss and Bird.20 Eqn. (2) then can be transformed 8 into the form of eqn. (1) with the following relation for 4 1 2 : B12 -13X1(X2 +B21x1)-1 ‘12 = 1+BX2(X2+B2,X,)-’ Bl2 and are related to b12 and P2 such that B12fBill = b129 (9) (1 1) B = B21p12(A1+L2)-1-1* (12) and the defining relation for B being 421 can be generated from 4 1 2 by interchanging the subscripts in eqn.(9). We can similarly transform the rigorous expression for the viscosity coefficient of a binary gas mixture as given by Hirschfelder, Curtiss and Bird9 Corresponding to eqn. (2) we get B12BAl = PZY (13) Pi2 = (1 +2Y’ttl +1112111P’’ (14) Pi = ( ? l I / V 2 ) ( W ) 2 (15) 4 2 = (1;1-Y’2q11)iB‘+Q’rl, (16) X h l +p;2x1xz + B Z , 2 1 2 X:+ bi2XiX2 +pix; ’ tlmix = where40 CONDUCTIVITY AND VISCOSITY OF GAS MIXTURES and Here y is in g cm-1 sec-1, p in dyne cm-2, R is the gas constant in erg mole-1 deg.-1, and other quantities are as defined before.Eqn. (13) can be rearranged in the form of eqn. (1) with the following defining relation for +i2 : B i z -B'Xl(X12 + BilX1)- +" = 1+B'Xz(X2+B;lX,)-1 ' where B;,+B;i1 = biz, B' Bf-1- 12 21 -Pi, and 4i1 can be derived from eqn. (20) by interchanging the subscripts. B' = B;1&2(y1+y2)-1-l. TEMPERATURE DEPENDENCE OF (bij AND 4; We assume A:2 and B:, to be temperature independent, an approximation which holds fairly well20 From eqn. (9) we find that 4 1 2 depends upon temperature only through B12, 2321 and B, and all these quantities are temperature independent if the ratios (pD12/jZT) and (jZl/jZ2) be regarded as temperature independent. These ratios are, however, temperature dependent to some extent in general. For those gases which behave like rigid spheres these ratios are rigorously temperature in- dependent.For other realistic potentials the temperature dependence is small and is likely to be less so if the molecules involved have comparable masses. Similarly, it can be shown that +b are also dependent upon temperature to a very small extent. This explains the success achieved in predicting high temperature data 9-11 on the basis of eqn. (1) with 4ij or 4; determined at some lower temperature. COMPOSITION DEPENDENCE OF 4ij AND 4; From eqn. (9) we find that the 412 depends upon composition through B12 and the factors SX&V2+&1X1)-1 = Y (say) and BX2(X2+&1Xl)-l = 2 (say). Now B12 depends upon composition only through D12 and as the latter has an extremely small composition dependence for most of the gas pairs, we can regard Bl2 to be composition independent.The quantities Y and 2 do depend upon composition and though their values are not always small compared to 2312 and unity respectively, yet their effect on the value of 4 1 2 with the change in composition is negligible. This is because Y and 2 act in opposite directions as X I changes, with the result that the ratio (Bl2 - Y)( 1 +Z)-1, and therefore 4 1 2 , remains insensitive to the composition. A similar discussion will lead to approximate composition independence of 4 z 1 . Table 1 illustrates this in a quantitative fashion for a few gas pairs. The com- puted values of 412 and 4 2 1 have been listed for the two arbitrarily chosen composi- tions.* It is seen that 4 1 2 and 4 2 1 both vary with composition to some extent.Usually this variation is small if the molecular masses of the two components in- volved differ widely. This is because in most such cases B is small. The maximum * These calculations are according to the modified Buckingham exp-6 potential and the para- meters used are reported by Saxena and Gandhi.21R . S . GAMBHIR AND S. C. SAXENA 41 variation obtained in the values of 412 and #21 with composition is for the Xe+Ar system for the nine systems considered in table 1. This variation is about 5.4 %, which though appreciable has little effect on the computation of Amix according to eqn. (1). The reason is in the systematic variation of $12 and 421 with composition. Thus, in table 1 we find that $12 increases with XI while 421 decreases so that they counterbalance the effect of each other.A similar discussion in connection with eqn. (20) also leads to the same conclusion that $;2 and are composition independent. TABLE COMPUTED VALUES (RIGOROUS, EQN. (9)) OF 412 AND $21 AS A FUNCTION OF COMPOSITION FOR NINE GAS PAIRS AT 18°C EXCEPT THOSE MARKED AS * REFER TO 38°C 412 421 gas pair XI = 0.1 Xi =0.9 XI = 0.1 x1 = 0.9 Xe+ He Kr+ He Ar+He* Xe+Ne Kr+Ne Xe+Ar Kr+Ar Ar+Ne* Xe+ Kr 0.3 18 0.465 0.682 0-933 0.797 0.928 0.982 0.796 0.964 0-3 19 0.465 0.696 0.934 0.81 8 0.98 1 1 -027 0.820 0.999 3.383 3.120 2.820 2.792 2.139 1.581 1.255 1 -495 1-196 3.384 3.125 2.675 2.757 2.034 1.496 1.199 1 -462 1.153 SIMPLER EXPRESSIONS FOR 4 i j AND 4h In general it is not possible to simplify eqn. (9) without making some assumptions.However, for those binary systems where M1%Mz it is possible to derive much simpler expressions for $ij without any appreciable loss of accuracy. For such systems it turns out that B is very small, with the result that Y and 2 are also small and negligible compared with B12 and unity, respectively. Eqn. (9) then simplifies to Further, for such systems (bf2-4Pz) is nearly equal to zero so that eqn. (24) assumes the simpler form : 4 1 2 N B 1 2 . (24) + 1 2 ~ B 1 2 = (b12+ Jb:2-4P2)(1/2), (25) 21 b I 2 / 2 = J K . Similarly it can be shown that Combining eqn. (4), (6) and (7) we get 4 2 1 = B21= U j B 2 . i1 15M~/2+(25/4-33B~2)M~+4A~2MlM2 = /L.2 15M;/2 + (2514 - 3B?,)M: + 4Ar2M,M2' A f2 and B;C, are almost temperature independent for realistic intermolecular poten- tials and can be assigned a constant value of 1.10 with fair accuracy.20 We can thus rewrite eqn.(27) as where 59M2 + 88M + 150 f(M) = 150M2+88A4+$9' In eqn. (28) and (29) M i s equal to MzlMl.42 CONDUCTIVITY AND VISCOSITY OF GAS MIXTURES To test the adequacy of these simpler expressions for 4 g j we have performed the numerical calculations for the He+Xe system at 18°C according to the modified expd potential in conjunction with the potential parameters given by Mason.22 For this system : B = 0.00337 and 4 1 2 = B12 within an accuracy of better than 1 % over the entire composition range. The numerical values are 0.317 and 3.371 for B12(~412) and B21(~421), respectively. For this system b6-4P2 = 0.000394, and 4 1 2 and 4 2 1 calculated on the basis of eqn.(25a) and (26) are 0.303 and 3.305, respec- tively. These latter values of 4 1 2 and 421 calculated with the knowledge of P2 only, given by eqn. (28) and (29), differ from the corresponding rigorous values (table 1) by about 3-5 % on the average. The percentage deviations in the calculated ;Imix values based on these approximate values for 4ij will be still smaller, as seen from table 2. Also recorded in table 2 are the values for this system at two other higher temperatures. The disagreement between the approximate and rigorous Amjx is somewhat pronounced at the highest temperature. The reason for this is that the factor (b&-4/32)* is no longer small as compared to b~2, and eqn. (25) and (25a) are invalid. TABLE 2.<OMPARISON OF RIGOROUS AND APPROXIMATE jZmix VALUES FOR THE Xe+He SYSTEM lo' jlmjx dev.mole fraction XI rig. approx.* 18 0.898 247 246 - 0.4 0.594 710 719 + 1.3 0.139 2378 2367 - 0.5 38 0.8991 261 252 - 3.4 0.4963 981 975 - 0.6 0.1 139 2665 2663 -0.1 520 0.798 832 883 + 6-1 0-582 1590 1696 + 6.7 0.21 3 3982 4220 + 6.0 % temp. ooc * values computed according to eqn. (l), (25u) and (26). The expressions for #J;* and are also simple for such systems where the ap- proximation M1+M2 holds. We now have RATIOS 4 r j l 4 j t AND 4bl4;i For thermal conductivity we can write after some straightforward algebra from eqn. (9) thatR. S. GAMBHIR AND S. C. SAXENA 43 From eqn. (33) the ratio 412/+21 depends upon composition through the factor (P+ X:>(P+p,X?)-l only, and is nearly independent of composition because both X2 and p2X; are small as compared to P.Around the middle composition this factor departs from unity almost by a negligible amount. In table 3 this factor is listed for nine different gas pairs and at three compositions. From the entries for those systems where Ml$+M2 (viz., He+Xe and He+=) the above approxim- ation holds well as the value of the ratio is very close to unity. For the other systems, the factor (P + X:>(P ~ p 2 X 3 - 1 still remains fairly independent of composition. TABLE COMPUTED VALUES OF THE FACTOR (P+X:)(P+/?~A~-I AS A FUNCTION OF COMPOSITION FOR NINE GAS PAIRS AT 18°C EXCEPT THOSE MARKED AS * REFER TO 38°C gas pair x1 = 0.1 x1 = 0.5 x1 = 0.9 Xe+He =+He Ar+ He* Xe+ Ne Kr+Ne Xe+Ar K r + k Ar+Ne* Xe+Kr 1.OOO 1 - 0 1 0.982 0-996 0.957 0-948 0.957 0.980 0.967 1~0o0 0.999 1.009 1 -003 1.015 1.008 1 -003 1.004 0.997 1.OOo 0.998 1 -045 1.007 1 -057 1.061 1 -047 1 -024 1-038 For all the nine systems, the average absolute deviation from unity is 2.4 % at XI = 0.1 ; 0.5 % at X I = 0.5 ; and 3.2 % at X I = 0.9.The deviation from unity is never greater than 6.1 %. We thus suggest putting this factor equal to unity in eqn. (33) so that we have 4 , 2 1 4 2 1 = 8 2 . (35) Now eqn. (35) is valid around room temperatures. Even at high temperatures, eqn. (35) will hold if the factor (P+X)(P+/3&)-1 in eqn. (33) is almost temper- ature independent. That this is the case can be established because when MI% Mz, B is very small, and for binary systems of comparable masses the temperature dependences of the various factors occurring in eqn.(33) themselves become small. A similar treatment for viscosity will lead to the relation where Eqn. (36) can be used in the foliowing simplified form with fair accuracy : (36j as for thermal conductivity. /32 and puted from eqn. (28) and (31), respectively. occurring in eqn. (35) and (38) may be com- DISCUSSION Only for a definite type of binary mixtures (MI > Mz) is it possible to derive simpler expressions for +ij and +& Even these expressions become relatively less accurate at high temperatures. The main success of the work described here lies in deriving more fundamental relations for the ratios 4121421 and +;&I. It is not44 CONDUCTIVITY AND VISCOSITY OF GAS MIXTURES possible to reduce these ratios to the two forms suggested earlier.Mason and von Ubisch 7 suggested that #121#21 = w 2 , and Wright and Gray * that (39) The relations of eqn. (39) and (40) are both obtained as a special case of eqn. (27) only when M1 = M2. On the other hand, eqn. (39) and (40) have both proved very successful in reproducing the experimental data with v = 1 in one case 7 and v = 0.85 in the other.9-11 The reason of this partly lies in the success of the form of eqn. (1) in reproducing LiX and qmiX data, and partly in the compensation of these somewhat unrealistic assumed relations for the ratios, qj12/421 and 4i2/&, by the use of one experimental AmiX or qmix around the middle composition t o evaluate the absolute magnitudes of 4ij or 4$.* We now suggest the relations given by eqn.(35) and (38) for the ratios, to be used in conjunction with the one mixture value around the middle composition. The middle composition value should be preferred for then the relations for the ratios hold relatively better. Rigorously speaking 4 1 2 and 4 2 1 are not equal to 4i2 and &, respectively, as also are their ratios, i.e., #12/421 # 4i2/4il. The latter inequality is because f ( M ) # f’(M). The approximate simplified expressions derived for 4; by Wilke 3 and 4fj by Mason and Saxena 6 tend to establish equality between 4; and 4ij. This is held approximately as shown by the numerical calculations of Saxena and Gambhir.23 We thank Prof. M. F. Soonawala for his interest, and the Council of Scientific and Industrial Research, New Delhi, for financial support. * However, if we treat v as a disposable parameter in eqn. (40) it is always possible to find a value of v for each mixture such that f ( M ) = (Ml/M2)1-~. This will explain partly the success of eqn. (40) with variable v in reproducing A&. 1 Sutherland, Phil. Mag., 1895,40,421. 2 Buddenberg and Wilke, Ind. Eng. Chem., 1949,41,1345. 3 Wilke, J. Chem. Physics, 1950,18,517. 4Brokaw, J. Chem. Physics, 1958,29,391. 5 Lindsay and Bromley, Ind. Eng. Chem., 1950,42, 1508. 6 Mason and Saxena, Physics Fluids, 1958, 1, 361. 7 Mason and von Ubisch, Physics Fluids, 1960,3, 355. 8 Wright and Gray, Tram. Faraiby Soc., 1962,58, 1. 9 Saxena and Gambhir, Proc. Physic. SOC., 1963, 81,788. 10 Saxena and Gambhir, Indian J. Pure and Appl. Physics, 1963, 1, 208. 11 Saxena and Gambhir, Indian J. Pure Appl. Physics, 1963, 1, 318. 12 Saxena and Narayanan, Ind. Eng. Chem. Fundamentals, 1962, 1, 191. 13 Srivastava and Saxena, Proc. Physic. SOC. B, 1957,70, 369. 14 Saxena, Indian J. Physics, 1957, 31, 597. 15Saxena, J. Chem. Physics, 1956,25, 360. 16 Srivastava and Saxena, J. Chem. Physics, 1957,27,583. 17Mason, J. Chem. Physics, 1958,28, 1ooO. 18 Muckenfuss and Curtiss, J. Chem. Physics, 1958, 29, 1273. 19 Mason and Saxena, J. Chem. Physics, 1959,31, 511. 2OHirschfelder, Curtiss and Bird, Molecular Theory of Gases and Liquids (New York, John 21 Saxena and Gandhi, Rev. Mod. Physics, 1963,35, OOO. 22 Mason, J. Chem. Physics, 1955,23,49. 23 Saxem and Gambhir, J. Appl. Physics, 1963,14,436. Wiley, 1954).

ISSN:0014-7672    

DOI:10.1039/TF9646000038

出版商:RSC    

年代:1964

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Heats of Formation of Metal Halides Tetrachlorides of Vanadium and Hafnium BY P. GROSS AND C. HAYMAN Fulmer Research Institute Ltd., Stoke Poges, Bucks. Received 29th July, 1963 The heats of formation of the tetrachlorides of vanadium and hafnium have been determined by burning the metals in glass apparatus in chlorine vapour in contact with liquid chlorine at 25°C. Vanadium tetrachloride was obtained dissolved in liquid chlorine, and the heat of forming this solution has been measured in separate experiments. The heat of interaction between chlorine and hafnium tetrachloride was shown to be negligible. The heats of reaction of the metals with liquid chlorine, subject to minor corrections for impurities, were found to be AHr(VC14) = -127-26f 0.20 kcal/mole and AH, (HfC14) = -227.58 &0.22 kcal/mole ; the corresponding values derived for the standard heats of formation are AH! (VC4) = - 136.2 kcal/mole and AH? (HfC14) = -236.7 kcal/mole.Apart from their intrinsic interest, the values for the heats of formation of the chlorides of vanadium and hafnium are also of practical importance in the metal- lurgy of these metals. Vanadium may be obtained via its chloride from ferro- vanadiuml; hafnium is prepared from the chloride, and its separation from zirconium by an exchange reaction involving the chloride has been proposed.2 No experimental value for the heat of formation of hafnium tetrachloride exists. The value accepted for the heat of formation of vanadium tetrachloride when the present experiments were begun depends on the value for the heat of formation of vanadium pentoxide and on solution measurements involving several reaction steps, some of which may not be very well defined.3 The heats of formation of the two tetrachlorides have now been determined by measuring the heat of reaction between the metals and chlorine in contact with liquid chlorine in glass reaction vessels.In addition to the combustion experiments, ‘‘ correction ” experiments are necessary to determine the heat effects due to the evaporation of chlorine into the originally evacuated combustion bulb and to its interaction (dissolution, wetting), if any, with the metal chloride which has formed there.Vanadium tetrachloride dissolves in liquid chlorine. Hafnium tetrachloride is insoluble in chlorine and its heat of interaction with it (wetting), as found by experiments, is negligible. Since neither of the metals burnt spontaneously in chlorine, a small piece of titanium (which does) was attached to the metal for the initiation of the reaction. EXPERIMENTAL APPARATUS The reaction vessels for the combustion of vanadium were similar to those previously used for the combustion of titanium,S and the vessels for the combustion of hafnium were identical with those used for zirconium4; similar vessels were used in the “ correction ” experiments. They were made from standard Pyrex tubing and consisted essentially of two bulbs initially separated by a thin glass barb which is broken for the combustion.The smaller bulb (5 ml) contains liquid chlorine ; the main bulb (60 ml), initially evacuated holds an alumina or beryllia crucible containing the metal to be burned. The crucibles had slots cut in their sides, so that solid reaction products could not impede the combustion ; 4546 HEATS OF FORMATION OF METAL HALIDES this was not necessary, however, for vanadium, which readily burned to completion, giving tetrachloride which could be seen condensing as a dark liquid on the walls of the vessel, and leaving no residue in the crucible. The calorimetric apparatus, of the totally submerged type, has been described pre- viously. ?he temperature was measured to within 2 x 10-4 deg., as before, by a carefully calibrated semiconductor resistance thermometer.The heat capacity of the calorimeter, determined by the usual d.c. method, was 2.52540f0.00012 kcal/deg. [l kcal = 4.1840 kjoules] in both series of experiments. MATERIALS High-purity iodide vanadium supplied by the Vanadium Corporation of America was used. The impurities were in p.p.m. Fe 10, Si 10, C 60, 0 450, N 10, H 2. The impurities in the hafnium, apart from 1.93 % zirconium, were in p.p.m. : N 18, 0 230, Fe 200, A1 50, W 32, Cu<25, Ti<25. The zirconium content of the hafnium sample was determined spectrographically by two methods: first, by adding titanium to the hafnium sample in sulphuric acid solution and comparing with binary zirconium+ titanium standard solutions; secondly, as a check, by adding further known amounts of zirconium to the hafnium solution and extrapolating backwards. The results of the two methods were in good agreement.High-purity iodide titanium was used. High-purity liquid chlorine was prepared as previously described.5 Vanadium tetrachloride was prepared by passing purified and dried cylinder chlorine over small pieces of vanadium (99-7 %) at 250-300°C. The product was fractionated in an atmospheie of chlorine, and finally freed from dissolved chlorine by repeated freezing and pumping. Hafnium tetrachloride was prepared in situ as in the combustion experiments and freed from chlorine gas and titanium tetrachloride by pumping. RESULTS VANADIUM TETRACHLORIDE Details of the vanadium combustion experiments are given in table 1, and of the correction experiments in table 2.For each combustion experiment and its corresponding correction experiment, the final states (total amount of vanadium, total amount of chlorine, total volume, temperature) were as close together as possible. The " heat absorbed " in the " correction " experiments require small second-order corrections arising from slight variations in temperatures and volunies TABLE 1.rOMBUSTION OF VANADIUM IN CHLORINE expt. no. wt. of vanadium, B wt. of titanium, B wt. of chlorine, f3 volume of bulb, ml heat evolved, C d 1 vc 0.89904 0.03 195 10.02 49.5 23 19.4 2 vc 0.84296 0.03121 9.46 49.7 2177.8 3 vc 0*80000 0.02565 8.91 5 5.0 2030-1 4 vc 0.75 102 0,02252 8-35 52.1 1904.8 TABLE 2.-CORRECTION EXPERIMENTS * exp t . wt. of wt. of volume of heat absorbed, no.vc14, B Clz, B bulb, ml cal 1 vs 3.40 7.52 50.6 51.63 2 vs 3.19 7.12 49.5 50.37 3 vs 3.03 6-68 55.7 57.20 4 vs 2-84 6.26 52.7 54.41 * In these experiments the weights of V (in VC14) and C1 (free and in VCl4) were the same as in the corresponding combustion experiments. The " heat absorbed " includes heat of evaporation of chlorine into the combustion bulb and heat of mixing of liquid chlorine and VC4.P. GROSS AND C. HAYMAN 47 between the two sets. Table 3 gives the resulting " correction heats ", the correc- tions for the heat of combustion of the titanium, and the final results for the molar (V = 50.942) heat of reaction of vanadium with liquid chlorine at 25"C, subject to a small correction for impurities present, In calculating the impurity correc- tions it was assumed that iron was in solid solution and that silicon, carbon, nitrogen, TABLE 3.HEAT OF REACTION OF VANADIUM WITH LIQUID CHLORINE expt.correction titanium corrected AH' no. heat, cal correction, cal heat, cal kcal 1v 52.8 - 121.7 2250.5 - 127.52 2 v 52.6 - 118.8 21 11.6 - 127.61 3v 58.3 - 97.7 1990.7 - 127.76 4 v 55.3 - 85.8 1874.3 - 127.13 mean value - 127.25 & *20 hydrogen and oxygen were present as vanadium compounds, oxygen initially as monoxide and finally as pentoxide. The data on the heats of formation of these com- pounds and of the chlorides of the metallic impurities were taken from the literature, where available, or else estimated. The total impurity correction is - 0.09 kcal/mole leading to a corrected value of AH;, = - 127-35 kcal/mole for the heat of forma- tion of vanadium tetrachloride from metal and liquid chlorine.For the standard heat of formation (from chlorine gas at 1 atm pressure) the difference in the heat content between liquid chlorine at 25°C and chlorine gas at 25°C and 1 atm (4.406 kcal/mole chlorine) has to be subtracted, giving finally AH&8(VC14, liquid) = - 136.2 kcal/mole. The total error in this value from all experimental measurements, including the heat-capacity determination, the impurity correction and the heat of evaporation of chlorine, is estimated to be not greater than 0.4 kcallmole. HAFNIUM TETRACHLORIDE The results on the combustion of hafnium are given in table 4. Three correc- tion experiments were made ; in one of these the combustion bulb contained hafnium chloride.No difference in the heat which could be ascribed to interaction between hafnium tetrachloride and liquid chlorine was found; the mean value for the TABLE 4."OMBUSTION OF HAFNIUM IN CHLORINE expt. no. 1 HC 2 HC 3 HC 4 HC 5 HC 6 HC 7 HC 8 HC wt. of metal (Hf and Zr), g 1.93612 1.58489 2.02268 1 -78039 2.020 17 2.1798 1 2.195 12 2.1 5647 wt. of m present, g 1.89875 1.5 543 0 1-98359 1 a74603 1.981 18 2.1 3774 2- 15276 2.1 1485 wt. Ti, g 0.03085 0.029 17 0.03434 0.02414 0.01 574 0.02 172 0.03943 0.03259 evaporation volume, d 60.4 54.4 56.3 53.6 57.5 60.9 57.9 54.2 heat evolved, 2548.9 2096.8 2690.5 2336.8 2606.2 2830.7 2926.2 2859.3 cal correction was 1.251 cal/ml evaporation volume at 25°C. Table 5 gives the correc- tions for the heat of burning the zirconium contained in the hafnium and of the titanium used as initiator ; the corrections for the heat of evaporation of chlorine into the bulb; the corrected heat of reaction of hafnium with liquid chlorine (in- cluding a further minor second-order correction) ; and the molar (Hf = 178.49)48 HEATS OF FORMATION OF METAL HALIDES expt.no. 1 HC 2 HC 3 HC 4 HC 5 HC 6 HC 7 HC 8 HC TABLE 5,HEAT OF REACTION OF HAFNIUM WITH LIQUID CHLORINE Zr heat, C a l 92-54 75.75 96-68 85-09 96.56 104.2 104.9 103.1 Ti heat, cal 117.5 111.1 130.8 91.9 59.9 82.7 150- 1 124.1 evaporation heat, cal 77.2 69.3 71.7 68.1 73.4 77.4 73-5 69.5 corrected heat, cal 241 6.5 1979.6 2535.1 2228.3 2523.5 272 1 *6 2745-1 2702.0 AH‘ kcal - 227.1 6 -2227.33 - 228.1 1 - 227.79 - 227.35 - 227.24 - 227.60 - 228.04 mean value -227.58 If *22 heat of reaction of hafnium with liquid chlorine at 25”C, subject to correction for impurities other than zirconium.For the impurity corrections, zirconium and titanium were assumed to be in solid solution and iron, copper, aluminium, tungsten, oxygen and nitrogen to be present as compounds. Tabulated or estimated values for the heats of formation were used. The total impurity correction is -0.35 kcal leading to a value for the heat of formation of hafnium tetrachloride from liquid chlorine of - 227.93 kcal/mole, so that one obtains for the standard heat of formation of hafnium tetrachloride AH;(HfCl,) = -236.7 kcal. The total error in this figure is considered to be less than 0.5 kcal. DISCUSSION VANADIUM TETRACHLORIDE At the time of completion of these experiments the only available experimental value for the heat of formation of vanadium tetrachloride was based on measure- ments by Ruff and Friedrich.3 These authors compared the heat of dissolving vanadium tetrachloride in an alkaline hydrogen peroxide solution with that of dissolving vanadium pentoxide in the same medium. From their comparison and a more recent6 value for the heat of formation of vanadium pentoxide AHf”(V205) = -372f7 kcal one obtains AHf”(VC14) = - 133 kcal/mole for the standard heat of formation of vanadium tetrachloride.Agreement between this value and our own is as good as might be expected in view of the large uncertainty in the value for vanadium pent oxide. However, more recently, a value AHf”(VC14) = - 149 kcal has been published by Shchukarev, Vasil’kova, Perfilova and Chernykh,7 who obtained well-reproducible values for the heat of dissolving vanadium trichloride in alkaline hydrogen peroxide solution, a reaction which had been found rather unsatisfactory by Ruff and Friedrich. By coniparing their result with new experiments on the heat of dissolving vanadium pentoxide in the same solution 8-which are in broad agreement with those by Ruff and Friedrich-and the heat of formation of vanadium pentoxide for which they take AHf”(V205) = -373 kcal they obtain AH:(VC13) = - 143 kcal for the heat of formation of vanadium trichloride.From the heat of formation of vanadium di- chloride AHf”(VCl2) = - 110 2 1 kcal9 derived from the temperature dependence and the absolute valui of the equilibrium constant of the reaction VC1,jsolid) + H, = V(so1id) + 2HCI,P.GROSS AND C. HAYMAN 49 and the heat derived from the temperature dependence of the equilibrium 2VC13 (solid) = VC12(solid) +VC14(vapour) at 540°C (AHr8300~ = 38 1 kcal) 10 they derived 6 kcal for the difference of the heats of formation of vanadium tri- and tetrachloride. It is not clear what value they used for the heat of evaporation of vanadium tetrachloride ; taking AH298(evap.) = 9.3 kcal,ll we calculate from their data a value of 1 kcal for this difference. A value of 2 kcal is obtained from the heat derived from the temperature dependence of the equilibrium 11 2 VC13(solid) + Cl2 = 2VC14(vapour) [AHp4400K = 13.8 kcal], and from this difference and our value for vanadium tetrachloride a value of AH?(VC13) = - 134 kcal is derived. From our value of the heat of formation of vanadium tetrachloride, its heat of evaporation,ll the heat of sublimation 13 of vanadium AH;(298)(V) = 122.7 and the usual value for the heat of formation of the chlorine atom 13 (28-9) one obtains for the bond strength in vanadium tetrachloride E(V-C1) = 91 kcal. HAFNIUM TETRACHLORIDE No previous experimental value for the heat of formation of hafnium tetra- chloride exists.It is of interest to compare the bond strength in zirconium chloride with that in hafnium chloride, although the latter is somewhat uncertain because of the uncertainty in the heat of sublimation of hafnium. Using our values for the heats of formation of the two chlorides AH598(ZrC14) = -234.7 kcal5 and AHj’298(HfC14) = -236.7 kcal, the heats of sublimation of the two 12 chlorides AH;(ZrC14) = 24.7 kcal and AH;(HfC14) = 23.8 kcal, and of the metals 13 AH&g8(Zr) = 142.5 kcal and AHf298(Hf) = 168 kcal one obtains for the bond strength in the two tetrachlorides E(Zr-Cl) = 117 kcal and E(Hf-Cl) = 124 kcal.The relatively high difference between them derives mainly from the difference in the heat of sub- limation of the two metals. We wish to thank the General Chemical Division of Imperial Chemical Industries Limited for their support of the work on hafnium and for their permission to publish these results. Our thanks are also due to the Vanadium Corporation of America, Cambridge Plant, Cambridge, Ohio, U.S.A., who provided us with the vanadium used in the experiments, to Dr. R. H. Gillette of European Research Associates who supplied us with the hafnium used in the experiments, and to the United States Bureau of Mines, Albany, Oregon, for a small button of hafnium with zirconium analysis used to confirm our analytical method. We are grateful to our former colleagues Mr. C. S. Campbell who developed the method for analysis of the zir- conium content of the hafnium and Mr. D. L. Levi for his co-operation throughout the investigation. 1 Tyzack and England, Symp. Extraction and Refitzing of the Rarer Metals (Institution of Mining 2 Prakash and Sundaram, Int. Con$ Peacefui Uses Atomic Erzergy (Geneva, 1955), A/Conf. 3 Ruff and Friedrich, 2. anorg. Chem., 1914, 89,279. 4 Gross, Hayman and Levi, Trans. Faraday Sac., 1955, 51, 626. 5 Gross, Hayman and Levi, Trans. Faraday Soc., 1957, 53, 1285. 6 Kubaschewski and Evans, Metallurgical Thermochemistry (London, 1958). 7 Shchukarev, Vasil’kova, Perfllova and Chernykh, Russ. J. Inorg. Chem., 1962, 7, 1509. 8 Shchukarev, Oranskaya, Vasil’kova, Tsintsiu and Subbotina, cited in ref. (7). 9 Shchukarev, Oranskaya, Tolmacheva and Il’inskii, Russ. J. Inorg. Chem., 1960, 5, 8. 10 Oranskaya, Lebedev and Perfilova, Russ. J. Inorg. Chem., 1961, 6,259. 11 Simons and Powell, J. Amer. Chem. Sac., 1945, 67, 75. 12 Palko, Ryon and Kuhn, J. Physic. Chem., 1958, 62, 319. 13 Stull and Sinke, Thermodynamic Properties of the elements (Washington, D.C., 1956). and Metallurgy, London, 1957), p. 175. 8/P/876.

ISSN:0014-7672    

DOI:10.1039/TF9646000045

出版商:RSC    

年代:1964

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Thermochemical Studies Part 2.-Thermochemistry of Some Transition Metal Tetrachloro-Complexes BY P. PAOLETTI AND A. VACCA Institute of General and Inorganic Chemistry, University of Florence, Florence, Italy Receiced 29th July, 1963 The heats of solution in water of the chlorocomplexes Rb2ZnCl.4, Rb2CoC4, CszZnC4, Cs2CoC14, (NMe&MIIC14 and (NEt&MJI(&, where MI1 = Mn, Fe, Co, Ni, Cu and Zn, were measured calorimetrically. From these values the heats of formation of the solid chlorocomplexes from the simple solid chlorides were derived.Assuming that the lattice enthalpies are equal in each of the two series of the complexes (NMe4)2MW& and (NEt4)2MIrC14 the dissociation enthalpies of the metal-chlorine bond in the Mn, Fey Co, Ni and Cu complexes were obtained relative to that in the Zn compound. Using the Kapunstinskii's equation, modified by Yatsimirskii, the lattice enthalpies of the complexes of Rb and Cs were calculated, and the thermochemical radii of ZnCli- and CoCI$- then obtained. By means of the appropriate thermochemical cycles the values of the dissociation enthalpy of the gaseous ions ZnClZ- and CoCl$- were obtained. The thermochemical radius of the NMet ion was derived. Few direct measurements of the strength of co-ordinate bonds have been made.1 The purpose of the present work is to determine by means of calorimetric measure- ments the metal-chlorine bonding energy in the tetrahedral complex ions having the general formula(MW14)2-, where MH is Mn, Fe, Coy Ni, Cu and Zn.In the solid state these anions are only stable in the presence of very large cations. The complexes examined were Rb2CoC14, Rb~ZnC14, Cs2CoC14, Cs2ZnC14 and two series of compounds Ml(MnC14) where MI is equal respectively to NMe4 and NE4. The only existing calorimetric values in the literature for these compounds in the solid state, are those reported in Selected Values of Chemical Thermodynamic Properties 2 for the chlorocomplexes of Cu with Rb and Cs. This is a particularly unfortunate choice, however, since the crystallographic data available for (CuC14)2- show that this ion is considerably distorted2 EXPERIMENTAL MATERIALS Reagent-grade RbCl and CsCl were used.The tetramethylammonium chloride was dried in a vacuum oven at 60" to constant weight (C4H12NCl: C1, 30.88 % found, 31.01 calc.). NEt4Cl. 4H20 was recrystallized several times from chloroform and the product was dried at 95" to constant weight (CsH20NCl : Cl, 21.44 % found, 21-4Ocalc.). An- hydrous MnC12 and CoC12 were obtained by allowing the corresponding hydrated salts to stand overnight in vacuum over H2SO4 and then heating at 250" for MnC12 and 140" for CoC12, in a current of hydrogen chloride.4 The compounds Rb2CoC4, RbzZnCh, Cs2CoCh and CszZnC4 were prepared as previously described.5 The complexes (NMe&MCb and (NEt&MCk, were obtained, according to the general procedure suggested by Gill and Nyholm,6 i.e., by mixing the stoichiometric amounts of the corresponding simple chlor- ides dissolved in ethyl alcohol.The compound (NMe.&NiCb was prepared by mixing alcoholic solutions of NMe4Cl and NiCl2 in the molar ratio 8 : 1. In order to eliminate the excess of NMe&I, the precipitate was boiled with isoamyl alcohol, quickly filtered, 50P. PAOLETTI AND A. VACCA 51 washed with light petroleum and dried in a vacuum oven at 60". With the FelI complexes particular care was taken in order to prevent oxidation: hydrogen was bubbled in the preparation vessel in presence of some drops of colloidal palladium. The complexes were analyzed by conventional methods for the halogen and the metal.The results of the analyses are given in table 1. compound C1 found 38.50 37.36 30.50 29.66 40.96 40.8 1 40.90 40.59 % talc. 38.15 37.50 30.40 29-98 41.10 41.00 40-63 40.66 TABLE 1 .-ANALYTICAL DATA compound MI* % found cdc. (NMe4)2CuCl4 mEt4)2MnCb 15.80 15-92 (NEt4)zCoCb 16.79 16.89 (NE~&CUC~ 17.33 17-29 (NMe&ZnCk 9.95 10.05 (NEt&FeC4 (NeT&NiCh (NEt4hznCb C1% found calc. 40.29 4 - 1 0 39-88 39.90 31-01 30.88 30.89 30.96 30-63 30.75 30.64 30.76 30.42 30.44 30.27 30.32 Mn %dc. found 17.89 17.95 18.08 18.39 11-92 12.01 12.17 12-19 12.93 12-78 12.72 12.73 13.59 13.64 13.90 13-97 CALORIMETRIC MEASUREMENTS The calorimeter and the general procedure used were described in previous papers.7.8 Tn each experiment the bottle was filled with a weighed amount of the complex or of the simple chloride, whilst the Dewar flask contained a weighed amount of water or of a metal chloride solution.With tetraeihylammonium chloride the bottle was filled in a dry-box and then left open in an oven at 95" until at constant weight. In the experiments carried out with the ferrous compounds oxidation was prevented by bubbling nitrogen into the calorimetric liquid. The solution of the solid salt was complete in 30 sec. In each experi- ment two determinations of the electrical-energy equivalent were made, and the reproduci- bility of this quantity was usually better than f0-2 %. RESULTS Heats of solution of NMe4Cl in the various metal chloride solutions were measured and found to be coincident, within the experimental error, with the value of the heat of solution in pure water.TABLE 2.-HEATS OF SOLUTIONu compound RbCl CSCl NMe4C1 NEt4Cl MnC12 FeC12 coc12 NiC12 cuc12 ZnC12 RbzZnCb Cs2ZnC14 RbzCoCld cs~coclL$ AH5 (kcallmole) 4.26 f 0.0 1 4.30 f0.02 1.1 1 f0.01 - 4.14&0.03 - 17.19 AO.01 - 19.3 - 19.35 - 19.46 - 12.20 - 16.52 3.56 f0.01 7-77 A0 09 - 5.04 f0.07 - 0.35 fO 02 AH5 (kcal/moIe) - 7.05fO05 - 80821.005 - 6*92+000 - 17.33 10.08 - 3.235002 1-39 f0.03 - 11-40 f0-04 - 13.17f0.06 - 11.29 f0.02 -21.41 h0.13 - 840fO-16 - 2.98fO01 a The molar ratio of the salt to water was 1 : 2000 except for the simple chlorides MCI for which b Nat. Bur. Stand., circ. 500. the ratio was 1 : 1OOO.52 BOND-DISSOCIATION ENERGIES The heats AHs of solution in water of the chlorides and the chlorocomplexes are listed in table 2.Each value is the average of at least two runs. The values for RbCl and CsCl are in good agreement with those reported in Rossini's survey 2 and the values for NMe4C1 and NEGC1 are in good agreement with those of Askew et al.9 DISCUSSION The enthalpy change for the formation of the solid complex from the simple solid chlorides, AHr 2M1C1+ M"Cl2-+M~(M"Cl4), has been derived using the formula, AH, = AH,(M "Cl,) + 2AHs(M 'Cl) - AHs(M,'M"CI4). The resulting values are listed in table 3. TABLE TH THE ENTHALPY CHANGES FOR THE REACTION 2M1C1+ MTTC12+M~/(MI1C14) MI* c o Zn Mn Fe c o Ni c u Zn -AHr (kcal/mole) 10.40 15.69 14-07 14.41 16.34 6.33 12.08 21.82 MI Rb Rb NMe4 NMe4 NMe4 NMe4 NMe4 NMe4 MI1 c o Zn Mn Fe c o Ni c u Zn -AHr (kcal/mole) 5.79 11-56 7.92 8.26 10.21 - 0.09 6.75 15.69 (1) difference (kcal/mole) 4-61 4.13 6-15 6.15 6.13 6.42 5-33 6.13 In the thermochemical cycle below, AHr 2M 'C1 + M I 'C12- +M~(M"Cl,) (solid state) $2AHt(M'CI) 4 AH[(MnC12) $ AHitM:(M"C141 2M+ + 2C1- + M2+ + 2Cl-- +2Mf + (M"C14)2- (gaseous state), AHl represent the lattice enthalpies of the species involved in reaction (1) and 45(M-C1) represents the enthalpy of dissociation of the gaseous complex ion.For RbCl, CsCl and the compounds MI'C12, the values of the lattice enthalpy were obtained from a Born-Haber cycle represented by the equation : AHl = L + ZI,, - n(E - 30) -AH,, in which L is the heat of sublimation of the metal, XIn the sum of the first n ionization potentials of the metal, E the electron affinity of chlorine, D the dissociation energy of the diatomic C12, and AHfis the heat of formation of the solid chloride.The values of these entities are shown in table 4. For the electron affinity of chlorine, Pritchard's value 10 (88-2 kcal) was chosen, as has been done in other recent studies,ll while for D the value reported by Cottrel12 (57.88 kcal) was adopted. The lattice enthalpy of the complex cannot be obtained by a similar method. Using two thermochemical cycles of the previously described type for the complexes (NMe4)zMnCh and (NMe&ZnC14 and making the hypothesis, which will be referred to later, that these two complexes have the same lattice enthalpy, then the expression, 4D(Mn-Cl) - 4D(Zn--Ci) = AH,[(NMe4),ZnC14] - AH,[(NMe,),MnCl,] + follows.46(M-C1) AH,(MnCl,) - AH,(ZnCl,)P. PAOLETTI AND A. VACCA 53 TABLE 4.-LAlTICE ENTHALPIES compound RbCl CSCl MnC12 FeCl2 coc12 NiC12 cuc12 ZnC12 L a 20.51 18.83 68 99 102 101 81 31-19 X I 2 96.30 89.77 532 555 574 595 646 63 1 AHf -102.91 - 103.50 C -115.19' - 81.86' - 77.80C - 72.97 C - 49.20 - 99.40 AH, 160.4 152.8 596.6 617.3 635.2 650.4 657.6 643.0 a Cottrel, The Strength of Chemical Bonds. b Nat. Bur. Stand., circ. 467. C Nat. Bur. Stand. circ. 500. dKoehler and Coughlin, J. Physic. Chem., 1959, 63, 605. e Busey and Giauque, J. Amer. Chem. Soc., 1953,75, 1791. Repeating these calculations for the pairs of the corresponding complexes of Fe+ Zn, Co+Zn, Ni+Zn and Cu+Zn, the values of the metal-chlorine bond strengths, relative to that of Zn, are obtained and reported in the penultimate column of table 5.Similarly, for the series of tetraethylammonium complexes, the values shown in the last column of table 5 are obtained. The agreement between the two series of values is excellent. TABLE 5.-RELATIVE VALUES OF THE DISSOCIATION ENERGY bond 45(M-C1)- 45(Zn-C1) (kcal/mole) Mn-Cl -54.2; -554.2 Fe-Cl -33.1 ; -33.1 co-"1 -13.3; -13.3 N i x 1 - 8.4; - 8.1 Cu-cl 5.7 ; 4.9 Subtracting the equation representing the thermochemical cycle of the type previously described, for the (NMe&MIrC4 complex, from the analogous equation for the (NEt4)2MI1CL.l complex having the same central atom, the equation : AH,[(NEt,),M "Cl,] - AH,[(NMe,),M "Cl,] = 2[AH,(NEt4C1) - AH,(NMe,Cl)] - (AH,[(NEt4),M"Cl4] - AH,[(NMe,),M"Cl,]) results.This difference is expressed by one constant term and another, the values of which are shown in the last column of table 3. With the exception of the value for the copper complexes, the latter term is practically constant, varying between 6.13 and 6-42 kcal/mole. This must mean, then, that either the lattice enthalpies are constant in each of the two series, as was previously assumed, or that they vary in a similar manner in the two series. The anomalous behaviour of copper is not surprising inasmuch as the tetrahedral anion (CuC14)2- is considerably distorted 3 and it is reasonable to assume that this distortion will vary with the counterion. Fig. 1 shows the curve obtained by plotting the relative values of the enthalpy of dissoci- ation against the atomic number of the metal.All the points fit on a smooth curve showing a monotonic rise from manganese to zinc, except that for copper which has an uncertain value owing to the assumption on which the calculation was based. The values indicated by half-filled circles are those obtained from the experimental data subtracting the crystal field stabilization energies (CFSE) which were obtained from the spectral data.13 All these values lie slightly above the straight line Mn - Zn, but this is not surprising as a similar behaviour was shown for the heats of formation of octahedral amino complexes 8 and also for the heats of hydration of the simple metal ions.654 BOND-DISSOCIATION ENERGIES In order to calculate absolute values of all the metal-chlorine bond energies, it would now be necessary to know the absolute value of that Zn-C1.For this purpose Kapun- stinskii's formula, modified by Yatsimirskii,l4 UI = 287*2Znp,p2[ 1 - 0.345/(rC+ rJ]/(r, + r,) + 2.5Znpu,p2 may be used. It enables the lattice energies of the complex salts to be determined. In this equation ZCn is the number of ions in the molecule, pl and pz are the charges on the ions and r, and ra are the radii of the cation and anion respectively. In consideration of the uncertainties in U f (complex), it may be assumed equal to AHi (complex). I t I I I I I I Mn Fe co Ni cu Zn for the crystal stabilization energy. FIG. 1 .-Relative bond dissociation energies of the ions MCli- : 0, experimental ; 0 , corrected The application of the two thermochemical cycles referred to above, for the complexes RbzZnC4 and CszZnCb, leads to the equations : -1l.S6+-[1-~]+15+4~(Zn-C1) 1723.2 = 2.160.4+643.0, 1.49 + x 1-49 + x -15*69+- 1723*2 [ l -- 0'345 ]+ 15 +4D(Zn-C1) = 2 .152.8 + 643.0, 1*65+x 1 * 6 5 + ~ where x is the value of the thermochemical radius of the ion (ZnC4)2-. By solving the sigultaneous equations, an acceptable value of 3.02 8, for x and a value of 607.6 kcal for 4D(Zn-C1) are obtained. The ratio between the thermochemical radius and the radius of the circumscribed sphere is 0.75 as is generally found for tetrahedral ions.15 The radius of the circumscribed sphere was obtained by adding the ionic radius of chlorine to the Zn-Cl distance, recently measured by Morosin and Lingafelter 16 in the complex (NMe,&ZnCL,.A similar Feries of calculations for the pair of complexes RbzCoCb, and Cs;?CoCb, gives a value of 3.14 8, for the thermochemical radius of the anion (CoCl@- and consequently a value of 602.4 kcal for the corresponding enthalpy of dissociation. Such a value is only 5.2 kcal lower than for the (ZnC14)Z- ion, whilst this difference calculated, assuming that the lattice enthalpies are equal, is 13.3 kcal (table 5). The absolute values of the dissociation enthalpy, however, depend on the choice of the ionic radii of Rb+ and Cs+. If we use the values obtained from the electron distribution maps, viz., 1.63 and 1.868, respectively,l7 instead of those of Goldschmidt,I* the values 666.2 and 658.6 kcal result for the dissociation enthalpies of (ZnCb)2- and (CoCl#-.P. PAOLETTI AND A.VACCA 55 Another result obtained was the value of the thermochemical radius of the tetramethyl- ammonium ion. By the usual process, the equation, -15*69+- 1723.2 -- 0.345 ] +15+607.6 = 2 . 574.4 -[1--]+10+&13.0, 0.345 x + 3.02 x + 3.02 x+1-81 x+1*81 was derived from the thermochemical cycle for the compound (NMe&ZnQ. In this equation, x represents the thermochemical radius of NMet for which a value of 2.10A is obtained, as the only acceptable root of the equation. Repeating the calculation for the complex (NMe&CoC14 a value of 1.93 A is found for x. The average value 2.02 f0.09 A is a reasonable one since it is in a ratio of 0.81 : 1 to the radius of the circumscribed sphere, as is expected for tetrahedral ions.15 The radius of the circumscribed sphere was calculated using Morosin’s value 16 for the C-N distance (1-55 A), a value of 1.09 A taken as a mean figure from Interatomic Distances 19 for the C-H distance and the ascepted value of 0.77 A for the covalent radius of C.We are indebted to Prof. L. Sacconi for helpful suggestions and criticism. Acknowledge- ment is made to the Italian “ Consiglio Nazionale delle Richerche ” for the support of this research. 1 Yatsimirskii and Astasheva, J. Gen. Chem. Russ., 1950, 20, 2219. Jones, Yow and May, 2 Rossini, Selected VaZues of Chemical Thermodynamic Properties (circ. 500, Nat. Bur. Stand., 3 Morosin and Lingafelter, J. Physic. Chem., 1961, 65, 50. 4 Mellor, Inorganic and Theoretical Chemistry (Longmans, London, 1961). 5 Gmelins Handbuch der Anorganischen Chemie, 8th ed., vol. 32 (Verlag Chemie, Weinheim, 6 Gill and Nyholm, J. Chem. SOC., 1959, 3997. 7 Sacconi, Paoletti and Ciampolini, Ric. Sci., 1959, 29, 2412. 8 Ciampolini, Paoletti and Sacconi, J. Chem. SOC., 1960, 4553 ; 1961, 2994. 9 Askew, Bullock, Smith, Tinkler, Gatty and Wolfenden, J. Chem. SOC., 1934, 1368. 10 Pritchard, Chem. Rev., 1953, 52, 529. 11 Ladd and Lee, J. Inorg. Nucl. Chem., 1959, 11, 264. 12 Cottrel, The Strengths of Chemical Bondr, 2nd ed. (Butterworths Sci. Publ., London, 1958). 13 Buffagni and Dunn, Nature, 1960, 186, 937. Furlani, Cervone and Valenti, J. Inurg. Nucl. 14 Yatsimirskii, Russ. J. Inorg. Chem., 1961, 6, 265. 15 Yatsimirskii, Thermochemie von Komplexverbindungen (German trans., Akademie-Verlag, 16 Morosin and Lingafelter, Acta Cryst., 1959, 12, 611. 17 Gourry and Adrian, SoZid State Physics, 1960, 10, 127. 18 Landolt-Bornstein, 6th ed., vol. 1, part 4 (Springer-Verlag, Berlin, 1955). 19 Interatomic Distances (Chem. Soc., London, 1958). Inurg. Chem., 1962, 1, 166. Washington, 1952). 1924); vol. 58 (Verlag Chemie, Berlin, 1932). Chem., 1963, 25,159. Berlin, 1955).

ISSN:0014-7672    

DOI:10.1039/TF9646000050

出版商:RSC    

年代:1964

数据来源: RSC

摘要:

118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility.The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order.The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point. These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure.This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13.118 ELECTRICAL THEORY OF ADBORPTTON The writer considers the double layer as consisting of a swface of rigidly fixed atoms under continuous bombardment of positively and negatively charged ions, any particular point on the rigid surface becoming in turn negative, neutral and positive, these conditions arisdg in any order. The observed contact difference is the average effect of these conditions. Where several kinds of atoms are present in the solution the average number of any one of them at the surface will depend on their concentbration, valency and mobility. The variation of contact Werence from negative to neutral and positive was observed with cotton and aluminium sulphate near the neutral point.These variations occurred during the same experiment, the readings being direct measurements of E.1I.F.s developed by filtration under pressure. This point would be covered by putting n2 = 1 and = 2 or 3 in Mukherjee’s equation No. 13. Calorimetric Determination of the Heats of the First and Second Ionization Stages of Salicylic Acid BY Z . L. ERNST, R. J. IRVING AND J. MENASHI Dept. of Chemistry, Battersea College of Technology, London, S.W. 11 Receired 25th September, 1963 A calorimetric method of determining heats of ionization of diprotic acids is described and has been used to measure the heats of ionization of salicylic acid, and the heat of solution of mono- sodium salicylate. At 25"C, we obtained : first stage of ionization, AH; = 0-73 k0.02 kcal/mole, second stage of ionization, AH; = 8.51 f0.08 kcal/mole, heat of solution of mono-sodium salicylate, AH: = 2-43 f0.02 kcal/mole.The ionization process of organic acids has been much investigated recently.1-6 Heat changes attending the ionization of acids are interesting, first, because they are more intimately related to bond strength than are free energy changes, and secondly, because they permit the calculation of entropy changes. In addition, heats and entropies of ionization provide information about the effect of substitu- tion on the strength of the acids of a homologous series, and on the stability of metal complexes in which the acids act as ligating agents. The purpose of the present paper is to describe a calorimetric method of measur- ing the heats of ionization of diprotic acids whose ionization stages do not overlap to any appreciable extent, e.g., salicylic acid.EXPERIMENTAL CALORIMETER The isothermal-jacket calorimeter is shown schematically in fig. 1. It is in principle the same as that described by Sunner and Wadso 7 and consists of a glass reaction vessel A of 100ml capacity. This vessel, which is fitted with an ampoule-breaking pin By is suspended from the lid of a surrounding chIomium-plated jacket C . The combined ampoule-holder and stirrer D is made of stainless steel and passes through the lid of the jacket into the reaction vessel. The thermistor (Stantel F 231 1/300) thermometer is rigidly mounted inside a thin-walled glass tube E in the reaction vessel.Its resistance can be measured to 0.01 $2 by means of a conventional Wheatstone bridge in conjunction with a Tinsley spot galvanometer. The uncertainty in determining temperature differences is estimated to be 0-0002"C. The electric calibration heater F consists of a lacquered nylon- spun manganin wire resistance RH = 50.745 Cl and is contained in another thin-walled glass tube in the reaction vessel. A dummy heater of the same resistance as the calibration heater is also provided. During the experiments the calorimeter was submerged in a thermostat at 25+0.OOl0C and the temperature of the calorimeter room was maintained at 23 *0.5"C. The reaction vessel was filled with 1OOml of standard HC104 or standard NaOH solution whose tem- perature was brought to 25°C with the aid of the calibration heater.A glass ampoule inserted centrally between the prongs of the stirrer contained a known amount of crystalline mono-sodium salicylate NaHSal. The reaction was started at the end of the initial period by breaking the glass ampoule and was taken to be completed when the resistance of the 56Z. L. ERNST, R. J . IRVING AND J . MENASHI 57 thermistor attained a steady value. The resistance-time curve for the “ after ” period was then recorded. Let q be the amount of heat liberated during the reaction and let Ri and Rj be the resistances of the thermistor at the commencement and at the end of the reaction respectively. If, as in the present case, Ri-&<75 0, we have 8 4 = c 1% (RilRf), (1 * 1) where C is a constant which incorporates the energy equivalent of the calorimeter and can be determined by calibration using the method of comparative measurements.9 During the precalibration period an electric current drawn from a d.c.stabilizer (Advance, type P.P.5) was passed through the dummy heater. When the current became constant it was switched over to the calibration heater for a definite period of time At. The amount of heat dissipated by the heater during that time was measured by comparing the potential drop across the heater with that across a standard resistance Y(= 0.99901 0). For this purpose a vernier precision potentiometer (Croydon Precision In- strument Co.) was used. Let Ri and Rf represent the resistances of the thermistor at the beginning and at the end of the calibration period respectively, then V2KHAt/r2j = C log (Ri/R>), where V is the potential drop across the standard resist- ance and j = 4,1840 abs.joules/cal.lo For the calibration of the calorimeter a current was selected such as to pro- duce a temperature rise as nearly equal to that in the actual reaction as possible. However, because of the rapidity of the reaction, it was not possible exactly to reproduce the resistance-time curve for the reaction in the calibration experiments. For this reason the observed temperature rise in both the actual runs and the cali- bration experiments was corrected for heat leakage and heat of stirring by the method of Dickinson.11 The uncertainty in the electric calibration is estimated to be 0.07 %. The duration of the calibration current was measured with an electrically operated (0.1 sec) stop-clock. The starting or stopping of the clock was synchronized with the operation of the calibration heater by means of a double-pole double-throw switch.Finally, the reliability of the calorimeter was tested by determining the heat of a known reaction. Recently, FIG. 1 .<alorimetric determina- tion of the first and second stages of ionisation of salicylic acid. Irving and Wadso 12 have proposed the heat of reaction of tris(hydroxymethy1) amino- methane with 0-1 M hydrochloric acid as a convenient standard, and this reaction was employed in the present work. Five measurements were carried out, from which the value AH = -7106&3 cal/mole was found, in agreement with the value -7104f3 cal/mole obtained by Irving and Wadso.Since salicylic acid is not readily soluble, crystalline mono-sodium salicylate was used ; under the conditions employed the dissolution took place in less than 20 sec. REAGENTS Mono-sodium salicylate was purified by repeated recrystallization from alcohol and dried in vacuo over P2O5. The purity of the product was tested by titration against standard alkali, using the method of Henville.13 Standard solutions of HClO4 and NaOH were prepared from A.R. reagents as described by Ernst and Menashi.1458 HEATS OF IONIZATION OF SALICYLIC ACID THEORETICAL Let H2L represent a diprotic acid with the dissociation constants where h = [H+] andfi andf2 are the activity coefficients of the singly and doubly ionized species respectively.On dissolving the mono-sodium salt of the acid in an aqueous solution of HC104 or NaOH the following reactions take place : NaHL(s) + Na+(aq) + HL-(aq) ; AH, ( 1) HL-(aq) + H+(aq) +HzL(aq) ; -AH1 (2) OH-(aq) + H+(aq) +H2O ; AHn (4) HL-(aq)+H+(aq + L2-(aq) ; AH2 (3) (2.2) where AH, is the heat of solution of the mono-sodium salt, AH1 and AH2 are the heats of the first and second stages of ionization respectively, and AHn is the heat of neutralization. All the enthalpy changes refer to unit amount of chemical reaction. Let q be the total amount of heat absorbed when Wg of the salt, of molecular weight M, are dissolved in 100 ml of the calorimeter solution (standard HC104 or NaOH solution), and let 41, q2, q 3 and q4 be the partial heat effects due to stages (I), (2), (3) and (4), respectively. Expressing the latter in terms of the enthalpy changes and amounts of the corresponding reactions, we have q1 = A€ISc/lO, 1 where [OH-]o and [OH-] are the OH- concentrations at the commencement and at the end of the reaction respectively, and c = 10 W/M is the stoichiometric con- centration of NaHL in the solution.Volume changes have been neglected. Since q is equal to the sum of the partial heat effects, then If, as in the present case, the two ionization stages of the acid are widely separated, i.e., if K2<K1, eqn. (2.4) can be considered under two extreme sets of conditions.14 (I) h29 KlK2; then both [OH-] and [L2-] are negligible and (2.4) simplifies to Also, as a result of the reaction, equivalent amounts of H2L and H+ are produced and consumed respectively, so that where p is the stoichiometric concentration of HC104.10q = AHSc-AH1[H2L] +AH2[L2-] +AH,([OH-]o- [OH-]). (2-4) 1Oq = AHSc-AH1[H2L]. (2.5) p 3 2 q = P-h, (2.6) Substituting this value into (2.5) and rearranging then The observed values of AH, and AH1 can be converted to the values which refer to the hypothetical standard state (denoted here by the superscript ") at infinite dilu- lOq/c = AH,-AHi(p- h)/c. (2.7) tion using (2.8) :Z . L . ERNST, R . J . IRVING AND J . MENASHI 59 where p is the chemical potential, the partial molar enthalpy, 5 the activity co- efficient of the ith species, and all other terms have their usual significance. Applica- tion of (2.8) to the present case yields AIfs = AH," -2RT2d(lnJo,1)jd?', AH1 = AH,"-2RT2d(ln fo,JdT, wheref0,l signifies the activity coefficient of a univalent ion at the commencement of the reaction.Substituting these values into (2.7) and rearranging, 10q/c+2RT2[1 -(p-h)jc]d(lnJ,,,)jdT = AH," -AH;)(p-h)/c. (2.11) The temperature coefficient of the activity coefficient at 25°C can be estimated by means of the approximate relation 15 whence (2.13) and (2.14) Putting Y = ~ O ~ / ~ + ~ . ~ 3 [ ~ - ( ~ - ~ ) l ~ l 1 o g , , f o , , (2.15) then y = AH," - AHY(p - h)/c (2.16) Hence, if y is plotted against (p-h)/c a straight line should result, with intercept and slope equal to AH," and AH; respectively. (a) h2< K1K2 ; here both h and [HzL] are negligible and eqn. (2.4) reduces to 1Oq = AH,c + AH2[L2- J + AHn( [OH-], - [OH-]).(2.17) Further, since as a result of the reaction, equivalent amounts of L2- and OH- are produced and removed respectively, and therefore lOq/c = AHs + (AH2 + AH,)(b - [ OH-]>/c, (2.i9) where b = [OH-]o and represents the stoichiometric concentration of NaOH. Finally, extrapolating to infinite dilution with the aid of eqn. (2.8) and (2.13), then 1%/~+O-814(10~1of& - [ ( b - [OH-])/'c3 h 1 0 (fo31/f1fi>3 = where the subscript 0 refers to the commencement of the reaction. Putting then whence AH; can be found either graphically or by applying the method of least squares. RESULTS AND DISCUSSION d(log,,fi)/dT = 2 x IoglOfi, (2.12) RT2d(lnfi)/dT = 0.814 loglof;. (kcal/moie), lOqjc+ 1-63[1 -(p-h)ic] loglojb,l = AH,"-AHi(p-h)jc. [L2-] = [OH-]o-[OH-], (2.18) AH," +(AH; + H",(b - [ OH-])/c (2.20) Y' = lOq/c+0.814(logl,f~,l- [(b- CoH-l>/~l log10 t&/W&, Y~ = AH," +(AH; + AH",(b - [OH- J)/c, (2.21) (2.22) FIRST STAGE OF IONIZATION OF SALICYLIC ACID The symbols H2L, HL- and L2- refer to the appropriate species of the salicylic acid.To determine AH," varying amounts of NaHL were dissolved in 100 ml60 HEATS OF IONIZATION OF SALICYLIC ACID of standard HClO4 solution and the amounts of heat q liberated measured. The H2L concentration of the solution is given by and hence, by comparing (3.1) with (2.6), [HA = hf?ci(K, + hf 3, P - h = hf W(K, + hf 3, (3.1) (3 -2) which equation can be solved for h by standard methods. The ionic strength of the solutions can be expressed by I =$(p+h+c+[HL-]), which in view of the electroneutrality condition simplifies to h+c = p+[HL---j, I = h+c (3.3) (3.4) (3.5) The activity coefficients of the charged species were calculated by means of the equation : 16 -loglo fi = O*5z2([I*/(l +I*)] -0.31). (3.6) The Hf concentration of the solutions at the end of the reaction was evaluated by successive approximations with the aid of eqn.(3.5) and (3.6). For this purpose, h was first put equal to p , and a rough value for I obtained from (3.5). This was then used to compute the requisite activity coefficients and subsequently an ap- proximate value for h by means of (3.2). The process of successive approximations was continued until the values for h from two successive approximation cycles agreed within 0.01 %. In these calculations the value 14 1-064 x 10-3 was adopted for Kl.In the last stage of the calculations AH," and AH," were evaluated by applying the method of least squares to eqn. (2.1). The precision of the experimental data was estimated by calculating the standard deviation 0, of y, and hence the standard deviations 17 aAH: and OAH:. The results are summarized in table 1, which shows the standard deviations of AH; and AH; to be 1 and 2 % respectively. In view of the small value of AH; the precision attained is regarded as satisfactory. TABLE HEAT OF THE FIRST STAGE OF IONIZATION OF SALICYLIC ACID 4 Y hx 103 *-v (g ion/].) (p--h)lc cxi03 pxi03 I0 I (mole/l.) (mole/l. Cal Xloz x102 7.694 9.780 1.458 1.747 1.169 1.873 +0*002 3.997 0.7516 8.925 9.780 1.724 1.871 1.230 1.905 -0.006 3.375 0.7177 10.865 4.890 2.379 1.576 1.166 2.136 +0*013 0.798 0.3766 12.269 2 - 4 5 2.916 1.471 1.255 2.306 -0.011 0.284 0.1761 12.286 0.196 3.058 1.248 1.231 2.411 +0*003 0.019 0.0143 AH," = 2.424 kcal/mole, AH; = 0.730 kcal/mole, u(AiYi) = f0.007 kcal/mole, o(AH;) = A-0.016 kcal/mole.SECOND STAGE OF IONIZATION OF SALICYLIC ACID To determine A H i varying amounts of mono-sodium salicylate were dissolved in 100 ml of standard NaOH solution and the resulting heat change q measured as described, The L2- concentration of the solutions is where Kw is the ionic product of water. By comparing (3.7 with (2.18), which can be solved for [OH-] by standard methods. [L2 -I = K2f? I: OH-lcl(Kw + K2f21 [OH- 11, b - [OH-] = K2f: [ OH-]C/(K, + K2fi [OH-]), (3.7) (3.8)Z . L. ERNST, R .J . IRVING AND J . MENASHI 61 The ionic strength of a solution containing NaHL at the stoichiometric concen- tration is given by which in view of (2.18) reduces to c = [HL-]+~L~--J (3.9) I = $(b + c +4[L2-] + [HL-] + [OH-]), (3.10) I = 2b+c-[OH-]. (3.11) The OH- concentration of the solutions was computed by successive approxima- tions using eqn. (3.8), (3.11), and the Davies activity equation.16 Next the values of y' and the corresponding values of (b - [OH-])/c were obtained and hence, by ap- plying the method of least squares to eqn. (2.22), AH; and AH; calculated. The values of K2 14 and Kw 18 were taken as 2.54 x 10-14 and 1.008 x 10-14, respectively, and that of AH: as 19 - 13.50 kcal/mole. The results are given in table 2, which shows that the standard deviation of both AH," and AH; is less than 1 %.Since AH; was measured in a pH range corresponding to a relatively small degree of dissocia- tion (12-33 %) such precision is satisfactory. Comparison of table 1 with table 2 shows that the values found in the present work for AH," are in good agreement with one another. There is also a good agreement between the present value AH; = 8.51 kcal/mole and the value 8-6 kcal/mole found by Agren 20 by means of the van? Hoff reaction isochore at an ionic strength of 3. TABLE 2.HEAT OF THE SECOND STAGE OF IONIZATION OF SALICYLIC ACID Ay' [OH-] lo' (b-[OH-]/c (g ion/].) Y' cxlO3 bxl02 4 10 I (mole/l.) (mole/l.) cal x 102 x 102 8.269 8.260 1-176 9,087 9.219 1.208 +Om014 8.056 0.2472 10.439 5.508 1.860 6.552 6.731 1.602 -0*004 5.329 0.1719 11.890 4.130 2.358 5.319 5.474 1.811 -Q*OO8 3.975 0.1308 11.703 3.304 2.451 4.474 4.597 1.946 -0.015 3.181 0.1051 11,304 0.083 2.498 1.213 1.216 2.428 +0-015 0.080 0.0025 AH: = 245 kcal/mole, AH" = 8-51 kcal/mole, AH: = - 13.50 kcal/mole.o(AH,") = rtO.01 kcal/mole, u(AH;) = f0.08 kcal/mole, The authors thank Dr. D. I. Stock for helpful discussions. 1 Canady, Papee and Laidler, Trans. Faraduy SOC., 1958, 54, 502. 2 Laidler, Trans. Faraday SOC., 1959, 55, 1725. 3 Mortimer and Laider, Trans. Fmaday SOC., 1959, 55, 1731. 4 Papee, Canady, Zawidski and Laidler, Trans. Furaday SOC., 1959,55, 1734. Zawidski, Papee, Canady and Laidler, Trans. Faraday Suc., 1959, 55, 1738. Zawidski, Papee and Laidler, Trans. Faraday SOC., 1959, 55, 1743. Sunner and Wadso, Acta Chem. Scand., 1959, 13, 97. Swietoslawski, Microcalorimetry (Reinhold, New York, 1946), p. 28. York, 1959), vol. 11, part 1, p. 530. * Skinner, Experimental Thermochemistry (Interscience Pubhhers, London, 1%2), vol. 11, p. 169. 10 Weissberger, Physical Methods of Organic Chemistry (Interscience Publishers, Inc. , New 12 Irving and Wadsij, Symp. Thermodynamics and Therrnochemistry (Lund, Sweden), 1963. 13 Henville, Analyst, 1927, 52, 149. 15 Scaife and Tyrell, J. Chem. SOC., 1958, 392. 16 Davies, Ion Association (Butterworths, London, 1962), p. 41. 17 Jerrard and McNeil, Theoretical and Experimental Physics (Chapman and Hall, London, 19 Papee, Canady and Laidler, Can. J. Chem., 1956, 34, 1677. 20 Agren, Svensk. Kem. Tidskr., 1956, 68, 181 , 185. 11 Dickinson, Nutl. Bur. Stand. Bull., 1915, 11, 189. 14 Ernst and Menashi, Trans. Faraday SOC., 1963, 59, 230. 1960), p. 13. 18 Harned and Robinson, Trans. Faraday SOC., 1940, 36, 973.

ISSN:0014-7672    

DOI:10.1039/TF9646000056

出版商:RSC    

年代:1964

数据来源: RSC